Which is the better juice, Goji, Noni or Mangosteen?

There is little scientific evidence that any of these juices work
against osteoarthritis (wear-and-tear-arthritis), although all are
bioactive and can have strong medical and medicinal effects.  But at
least one has an attractive affiliate program. ;)

Noni especially is problematic, especially if you take medicine for
high blood pressure that can change your potassium levels.  Mueller
BA, Scott MK, Sowinski KM, Prag KA. Noni juice (Morinda citrifolia):
hidden potential for hyperkalemia? Am J Kidney Dis 2000;35:310-2.

Goji juice is high in antioxidants, including beta-carotene and
ascorbic acid, but has been reported to interact with both diabetes
and hypertension medications.

And mangosteen is probably the least studied, but I know of no data to
support either antioxidant, anti-inflammatory or eicosanoid activity
in the knee or elsewhere, in the specific case of osteoarthritis.

Other references below.
Good luck!

An excellent arthritis eating plan:
www.KneeLife.com

A primer on treatment of osteoarthritis nutrition
http://en.wikipedia.org/wiki/Osteoarthritis#Dietary

Arthritis Foundation Guide to Alternative Medicine
http://www.amazon.com/exec/obidos/tg/detail/-/0912423234/104-2797390-5065555?v=glance

There is scientific research to support medical benefits of
Mangosteen, no current studies exist to prove arthritis benefits,
although, having anti-inflamatory benefits, it may help...I've taken
Xango juice supplements and have not had any of the knee problems I
had prior to taking the mangosteen based juice.

The only reference I've found that may help is: 
Gopalakrishnan C, Shankaranarayanan D, Kameswaran L, Nazimudeen SK.
Effect of mangostin, a xanthone from Garcinia mangostana Linn. in
immunopathological & inflammatory reactions.
Indian J Exp Biol. 1980 Aug;18(8):843-6. No abstract available. 
PMID: 7461736 [PubMed - indexed for MEDLINE]

Other articles to look up on mangosteen health benefits: 

"Xanthones from the Green Fruit Hulls of Garcinia mangostana." by:
Sunit Suksamrarn,*,? Narisara Suwannapoch,? Piniti Ratananukul,?
Nantana Aroonlerk,? and Apichart Suksamrarn§
Department of Chemistry, Faculty of Science, Srinakharinwirot
University, Bangkok 10110, Thailand, Department of Stomatology,
Faculty of Dentistry, Srinakharinwirot University, Bangkok 10110,
Thailand, and Department of Chemistry, Faculty of Science,
Ramkhamhaeng University, Bangkok 10240, Thailand
Received November 9, 2001

Abstract: Three new xanthones, mangostenol (1), mangostenone A (2),
and mangostenone B (3), were isolated from the green fruit hulls of
Garcinia mangostana, along with the known xanthones,
trapezifolixanthone,
tovophyllin B (4), R- and â-mangostins, garcinone B, mangostinone,
mangostanol, and the flavonoid epicatechin. The structures of the new
xanthones were elucidated by analysis of their spectroscopic data.

Three Xanthones and a Benzophenone from Garcinia mangostana
Yu-Ling Huang,*,? Chien-Chih Chen,? Ying-Jen Chen,? Ray-Ling Huang,?
and Bor-Jinn Shieh? National Research Institute of Chinese Medicine,
No. 155-1, Sec. 2, Li Nung Street Peitou, Taipei, Taiwan, Republic of
China,
and Department of Chemistry, Chung Yuan Christian University,
Chung-Li, Taiwan, Republic of China Received December 8, 2000

Abstract: Investigation of the constituents of Garcinia mangostana has
led to the isolation of four new compounds:three minor xanthones,
garcimangosone A (1), garcimangosone B (2), and garcimangosone C (3),
and a benzophenone glucoside, garcimangosone D (4). The structures of
these four compounds were established
by spectral (NMR and MS) and chemical methods.

There is also a liquid supplement called Seasilver which is comprised
of Aloe Vera, Sea Vegetables, Pau D'arco herb & fruit juice
concentrate.  The Aloe Vera & Pau D'arco are both anti-inflammatory
agents which could possibly help.  The products sells in a 32oz bottle
taking 2oz per day.  Currently there is a Buy 1 Get 1 Free product, so
you can get 2 for $40 which really helps your pocket and your body can
really get a good start on the product to feel the results your are
seeking.  This supplement has almost every major vitamin, mineral and
amino acid there is and it's free shipping/no sales tax.  All kinds of
incentives to get you started.  The web site is www.sipnutrition.com 
I do know someone that is currently taking Seasilver for the arthritis
and she keeps it stocked at all times.

Also you should take fish oil which lubricates the joints.  I have
heard that Omega XL supplements are really good too.

Avoid nightshade plants--tomatoes, eggplants, white/red potatoes,
peppers and I've heard orange juice too.  Do a trial on these
different foods to see which ones you may be allergic to.