How many objects (e.g. coins on a table) is it possible to estimate at
a glance, without counting?

That's an interesting question. I'd say "Quite a lot" The example that
comes to mind is arial population counts, eg crowds/ mobs, a herd of
elk, etc. The real question comes in with accuracy and precicion of
the count. I guess experience would play a large role in such "at a
glance" estimates, but that the degree of uniformity of the
'picture'(are the objects all the same size (just quarters, or
quarters and dimes) and how evenly spatially distributed they are
(bunched, up or evenly spread out) would also be important. Maybe do
some looking into Image Analysis.

some interesting info on this from:
http://www.centreforthemind.com/publications/IntegerArithmetic.cfm
"babies and animals can estimate the number of objects in a collection
with an error that is proportional to the number itself. This turns
out to be accurate for perceiving and estimating 1, 2 or 3 objects but
is grossly inaccurate for judging large numbers."
"Sacks (1985) observed autistic twins who could exchange prime numbers
in excess of eight figures, possibly even 20 figures, and who could
"see" the number of many objects at a glance. When a box of 111
matches fell to the floor the twins cried out 111 and 37, 37, 37.
Similar skills were reported as early as 1801 about a child named
Dase, who was also "singularly devoid of mathematical insight" and of
low general intelligence (Treffert 1989, Myers 1903)."

and:
http://www.telegraph.co.uk/connected/main.jhtml?xml=%2Fconnected%2F2004%2F05%2F05%2Fecfgorilla05.xml
"There have been some arguments that limits on visual memory are
related to limits on the number of items we can attend to at once as
well as to limits on the number of items we can count at a glance
(typically both have capacity estimates of around three to four),"
added Dr Simons.

The expert's e-mail can be found on
http://viscog.beckman.uiuc.edu/media/dailytelegraph.html

Good luck :)

I have seen estimates as high as seven. However there is bound to be
variation from person to person, and maybe it will vary with the typew
of object, how they are arranged etc.. The question as it stands is
really not answerable in an absolute sense.