Which species (animal, bird, fish, insect, reptiles, crustaceans etc)
and sub-species (dog, sparrow, shark etc) do NOT practice territorial
privacy (PI).  PI is the claim to privacy of a defined area made public
in some way-such as bees use pheremones to deter trespassers or
predators?

Are you looking for examples of specific species don't exibit
teritorial behavior? Surely, a complete list would be impossible, as
the number of species on Earth is estimated in at anywhere from 2 to
100 million.

Also, it would be good if you could clarify which classification level
you're interested in, as your listing is a bit confusing. Birds are
also animals, they are a class, while animals would be a kingdom. Dog
is not a sub-species but an order.

More info on Kingdom/Phylum/Class/Order/Family/Genus/Species classification at: 

http://www.emc.maricopa.edu/faculty/farabee/BIOBK/BioBookDivers_class.html

Here are a few facts to get you started.

http://www.biology.eku.edu/RITCHISO/behavecolnotes4.htm

"Decisions animals must make:  
1 - Whether or not to be territorial 

2 - If so, what size territory to defend"

[edit]

"How large should a territory be? 

Historically, the choice was viewed in terms of two competing hypotheses: 

1 - Adjustment of size in response to resource density 
2 - Adjustment of size in response to costs of defense 
Hypothesis 1 - Animal adjusts territory size to the density of the
critical resource (usually food) so territory contains enough to
satisfy requirements

Experimental evidence: 
Territory size (or home range size) is positively correlated with body
weight in a wide variety of animals (e.g., birds; Schoener 1968).
Resource analyses often reveal that territory sizes are smaller where
food is more abundant or nutritious. For example:
Simon, C.A. Ecology 56:993-998. Influence of food abundance on
territory size in the iguanid lizard Sceloporus jarrovi
Experimental manipulation of food supply: 
More food supplied ---> territories became smaller 
Food removed ---> territories became larger"

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An Overview of Insects Territoriality - Jeff Brase
http://www.colostate.edu/Depts/Entomology/courses/en507/papers_1995/brase.html

Summary:

Territoriality in insects is not as clearly studied as in vertebrates.
 Some of the reasons for this is the difficulty in studying insects in
their natural environment due to size.  Insects exhibit the behavior
of territoriality by defending resources such as feeding sites,
females and oviposition sites.  The defense of these resources
includes the use of advertisement that can takes the form of either
physical conspicuousness, acoustic signaling and scent marking. 
Insects can use one or all of these forms of advertisement.  In a few
instances when advertisement fails
the insect will engage in physical combat and only in a few cases do these 
engagements end in death.  There are many aspects of territorial
behavior such as body size, habitat quality, and cost of defense. 
Territoriality behavior is a wide subject with lots of potential for
further study.

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BEARS ARE NOT TERRITORIAL
http://www.goseebears.com/behave.htm.

Being territorial means keeping other members of your species away
from a given area. Wolves and primates are territorial - bears aren't.
Bears, like people, share home ranges. This mutual use of land and
resources is a basis for bear social behavior.

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http://www.the-aps.org/education/integweb/jclarke.htm

Ptarmigan are birds that live in alpine (that is, mountainous)
environments. One reason that Jennifer likes studying ptarmigan is
that they accept having observers around them. This makes them good
study animals. As Jennifer began studying the ptarmigan in the
Sierras, she discovered that they were so spread out that they really
did not exhibit any territorial behaviors.

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(Cached page... copy and past url)

http://216.239.57.104/search?q=cache:o9T6y3dkO6kJ:kingfish.coastal.edu/biology/bio460/notes/13territory.pdf+territorial+behavior+in+all+species&hl=en

The sanderling, an example of a bird with plastic territorial
behavior(sometimes territorial, sometimes not territorial, sometimes
they flock) when are sanderlings territorial ?  the Goldilocks rule.

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http://sites.state.pa.us/PA_Exec/PGC/w_notes/woodduck.htm

"The wood duck feeds along shores of woodland streams and ponds..."

[edit]

"When the birds migrate north, the hen homes in on last year's nest
tree, or, if she is a yearling, on the same general locale in which
she was hatched. The male sets up no actual territorial boundaries,
but will defend his mate from the attentions of other males."

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http://fishenthusiast.com/fishindex/discusturqinfo.html

The Discus Fish is a very peaceful fish, and only becomes territorial when breeding.

Yes, a complete list is impossible.  I've found more information to help you. 

Social status regulates growth rate: Consequences for life-history strategies
http://www.pnas.org/cgi/content/abstract/96/24/14171

The life-history strategies of organisms are sculpted over
evolutionary time by the relative prospects of present and future
reproductive success. As a consequence, animals of many species show
flexible behavioral responses to environmental and social change. Here
we show that disruption of the habitat of a colony of African cichlid
fish, Haplochromis burtoni (Günther) caused males to switch social
status more frequently than animals kept in a stable environment. H.
burtoni males can be either reproductively active, guarding a
territory, or reproductively inactive (nonterritorial). Although on
average 25-50% of the males are territorial in both the stable and
unstable environments, during the 20-week study, nearly two-thirds of
the animals became territorial for at least 1 week. Moreover, many
fish changed social status several times. Surprisingly, the induced
changes in social status caused changes in somatic growth.
Nonterritorial males and animals ascending in social rank showed an
increased growth rate whereas territorial males and animals descending
in social rank slowed their growth rate or even shrank. Similar
behavioral and physiological changes are caused by social change in
animals kept in stable environmental conditions, although at a lower
rate. This suggests that differential growth, in interaction with
environmental conditions, is a central mechanism underlying the
changes in social status. Such reversible phenotypic plasticity in a
crucial life-history trait may have evolved to enable animals to shift
resources from reproduction to growth or vice versa, depending on
present and future reproductive prospects.

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http://www.bbc.co.uk/nature/wildfacts/factfiles/193.shtml
Behaviour
Hedgehogs are solitary, non-territorial animals and are most active at
night after heavy rainfall.

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http://www.ctap3.org/_lperry/africa/moreanimals.htm.
CAPE BUFFALO (Nyati): They live in swamps, montane forests, flood
plains and wet savanna areas. These animals are very sociable and live
in large, mixed herds. They are non territorial.

RHINOCEROS (Kifaru): The Black Rhinoceros sometimes live in the forest
and other times in semi desert areas or wetlands. Sometimes they live
alone and are territorial, while other times they live with others and
are non territorial.

http://www.ctap3.org/_lperry/africa/animals.htm
GIRAFFE (Twiga): They live in dry savanna areas as long as there are
trees. They are herbivores, or plant eaters, and spend most of their
time browsing, nibbling on buds and leaves of the acacia tree. They
are non territorial and live in large herds with males and females of
all ages living together.

=================================================

http://www.awf.org/news/58.
Little else besides color patterns separates the various subspecies of
giraffe, all sociable, nonterritorial animals that spend up to 20
hours a day feeding on the leaves of thorny acacia trees and
occasionally ..."
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http://www.flmnh.ufl.edu/fish/Gallery/Descript/NassauGrouper/NassauGrouper.html
Grouper
There is a white band that reaches from the snout, past the eye
towards the dorsal fin. After swimming away, the bicolored fish
resumes its normal barred pattern within minutes. This same bicolored
pattern is observed in aggregations of spawning fishes, perhaps
indicating a peaceful, non-territorial state.

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http://fwie.fw.vt.edu/WWW/esis/lists/e254004.htm
Species DARTER, SNAIL

HOME RANGE/TERRITORY:  Non-territorial 

=================================================
http://www.bio.ulaval.ca/ecoscience/ARTICLE_ENG/vol2n2.htm
Ripple communication in aquatic and semiaquatic insects

Abstract: Among insects, ripple communication has been described in
water striders (Gerridae) and giant water bugs (Belostomatidae)..."

[edit]

"In various species, experimental playbacks of signals have
demonstrated functions of attraction of females by males, induction of
oviposition, sex discrimination, mate-guarding, enhancement of female
foraging, nonterritorial individual spacing, and intra- and
interspecific territoriality."

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http://www.cordio.org/Indian%20Ocean%20Islands%20-%20text%20only.htm.
The population of the non-territorial grazing herbivorous fish
Ctenochaetus striatus was significant in Planch?alizé (700
individuals).

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http://web.uct.ac.za/depts/fitzpatrick/docs/r269.html
Marsh Sandpiper Tringa stagnatilis
Generally non-territorial and not aggressive; occasional instances of
territoriality (eg Senegal R delta, Senegal) though to be facilitated
by complex habitat mosaic creating natural, defendable boundaries

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http://www.nps.gov/npsa/book/pdfs/marine.pdf
Many other species of coral reef fish are also algae eaters and two
general patterns of feeding have evolved among these species.  One is
for a species to become territorial and fiercly guard it's own algal
patch, and the other is to be non- territorial and roam around the
reef looking for an unguarded patch of algae to eat.

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https://article.pubs.nrc-cnrc.gc.ca/ppv/RPViewDoc?_handler_=HandleInitialGet&journal=cjz&volume=77&calyLang=eng&articleFile=z99-013.pdf&secure=true
Territorial loons and nonterritorial loons were present on most of the
lakes surveyed

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http://pubs.nrc-cnrc.gc.ca/cgi-bin/rp/rp2_abst_e?cjz_z01-054_79_ns_nf_cjz6-01
Territorial defense by coyotes (Canis latrans) in Yellowstone National
Park, Wyoming: who, how, where, when, and why

Territoriality was advantageous in that territory holders generally
had higher survival rates (except pups), contributed all the
reproductive effort to the population, and had greater access to food
resources. In contrast, nonterritorial animals had lower survival
rates, did not breed, and had reduced access to food (ungulate
carcasses) during winter.

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http://216.239.57.104/search?q=cache:IJLqW54JDeIJ:www.szgdocent.org/RATS/RATS2003/quiz_projects/Docent_Deluge_2003_Apr_27.ppt+non-territorial+animals&hl=en
The Eagle Owl - They are non-territorial and do not aggressively
protect their spaces.

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http://www.wildlifesafari.info/reedbuck_mountain.html
Mountain Reedbuck - Redunca fulvorufula 
The social organisation consists of territorial males, non-territorial males..."

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http://www.press.jhu.edu/books/walkers_mammals_of_the_world/artiodactyla/artiodactyla.bovidae.html
Antelope, Cattle, Bison, Buffalo, Goats, and Sheep

According to Estes (1974), most species of Bovidae are gregarious and
territorial. Exceptions include most species of the subfamily Bovinae,
which are either gregarious and nonterritorial or, in the case of
Tragelaphus scriptus and T. spekei, solitary and nonterritorial.

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http://powell.colgate.edu/wda/IJO_Instructions_to_authors.htm

Fincke, O.M., 1988. Sources of variation in lifetime reproductive
success in a nonterritorial damselfly (Odonata: Coenagrionidae). In:
Clutton-Brock, T.H. (ed.) Reproductive success, University of Chicago
Press, Chicago, pp. 24-43.

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http://www.fortworthzoo.com/conserve/survival.html
Bongo (Tragelaphus eurycerus)
Bongo in general are gregarious and nonterritorial.

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http://pacificislands.fws.gov/wesa/whteyeindex.html
Guam Bridled White-Eye / Zosterops conspicillatus / Nosa

"The white-eye is nonterritorial even when nesting, and has a low
volume contact call which is voiced frequently..."

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http://www.u.arizona.edu/~abadyaev/pubs/43.pdf
Most species of finches are nonterritorial, and song is primarily used
for female attraction and female stimulation (e.g., Newton 1973)
rather than for male competition. 

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http://www.epa.gov/fedrgstr/EPA-IMPACT/2004/March/Day-05/i4902.htm
If bald eagles successfully breed and create territories, they may be
able to discourage future colonization by nonterritorial golden
eagles.


Best regards,
tlspiegel

http://www.hibernationstation.com/

If you would like to see Bears in Yellowstone contact us at the
address above and we will direct you to the spots you will see bears.
Most people are seeing both Grizzley and Black bears. The best time to
see them in Yellowstone National park is late April through June. The
population is becoming so great that if you go were we direct you it
is likely to see at lease 1 bear but many times up to 10 bears in a
day.

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