Details, Documentation:

1st Place: peregrine falcon
There is a wide range of opinion on this bird's top speed, but very few sources put the number below 200 mph.  Some go as high as 280 mph.  This ludicrous speed is achieved only in a dive.  If you think dive speed shouldn't count, it still wouldn't change this bird's placing.  Even cruising it's the fastest.

2nd Place (tie):  cheetah, sailfish
Just about everyone puts the speeds for these two animals in the upper 60's

4th Place:  thoroughbred   *insects could possibly place fourth. See note at bottom of the dragonfly documentation
It is very difficult to find any documentation of a horse's speed without a rider.  The reason is nobody GAMBLES on horses without riders so there's no reason to do any such studies.   The numbers range from around 45 to 55 mph, so I feel safe placing the thoroughbred above the greyhound.  Here's some sources:

"The top speed of a of a Horse is about 45 Mph (70 Kph)"
http://www.irishhorsesociety.com/horsefacts.htm

"horse can sustain a racing gallop of nearly 70 km/hr" (45 mph)
http://www2.truman.edu/~capter/jins343/week2-3.pdf
This paper is really great.  Check out pg. 7 for info on horse locomotion vs. other animals

history of the Thoroughbred breed: http://www.imh.org/imh/bw/tbred.html#hist

Iowa American Quarter Horse Racing Association claims, "the American Quarter Horse rockets from starting gate to finish line at speeds up to 55 mph."
http://www.iqhra.com/

ESPN article claims "American Quarter Horses have been clocked at nearly 50 m.p.h. as they cross the finish line."
http://espn.go.com/horse/000420AQHASpecial.html

I know quarter horses are not technically thoroughbreds, but the horses could enter a quarter horse in the race if you had a problem with it.  And those numbers are with a rider.

5th Place:  greyhound
A lot of sources said 39 mph, some said up to 45 mph, but this article seemed thourough and placed greyhound speed at 43 mph:
http://www.fastdogs-fastfriends.com/medical_update.htm
Strangely, this same article states that, "A thoroughbred racehorse can achieve a maximum speed of around 49 kmh (30 mph)," which is pretty far off.  I don't know where they came up with that number.  Just calculating times from the Kentucky Derby will get you a higher number than that.

6th Place:  Australian Dragonfly
Many reliable sources put Aust. Dragonfly speed at 36 mph,but there is considerable debate over reliability of insect speed data.  Here's a great article on the issue from the University of Florida:
http://ufbir.ifas.ufl.edu/chap01.htm

Note: The above article believes the speed of the black cutworm moth (60 - 70 mph) to be authentic.  If that is true, then the insects could conceivably finish in fourth place, ahead of horses and greyhounds.  picture of the black cutworm moth: http://www.ent.iastate.edu/imagegal/lepidoptera/bcutworm/3936.106bcwormadult.html

7th Place:  Killer Whale
30 mph.  Originally, I had the fastest whale, the fin whale, swimming in this race.  But then I thought I'd lump all sea mammals together and therefore be able to enter a killer whale, which is faster than a fin whale and way cooler.  (Killer whales are members of the dolphin family)  Now, I know what you're thinking.  Why didn't I enter a Commerson's dolphin, which is clearly the fastest sea mammal?  Apart from being less cool, the faster Commerson's dolphin at 35 mph still wouldn't have placed differently in the race.
http://www.seaworld.org/infobooks/KillerWhale/adapaqkw.html

8th Place:  Deion Sanders
In his prime, my man ran about a 4.1 40.  40 yards in 4.1 seconds = approx. 23 mph

9th Place:  Nile Crocodile
11 mph.  Crocodile/ alligator speed is widely believed to be much higher than it really is.  Even seemingly reliable sites like the Everglades National Park site claims that alligators can reach speeds of 30 mph over short distances ( http://www.nps.gov/ever/eco/gator.htm ).

Here's a thorough article on crocodile locomotion and top speed (from University of Fl):
http://www.flmnh.ufl.edu/natsci/herpetology/brittoncrocs/cbd-faq-q4.htm
Quote from the article: "Most crocodiles can achieve speeds of around 12 to 14 kph (7 - 9 mph) for short periods, which is somewhat slower than a fit human can run. Don't believe the hype - if you're reasonably fit, you can definitely outrun a crocodile! Even faster are galloping crocodiles, and Australian freshwater crocodiles have been clocked at just over 17 kph (11 mph) over distances of perhaps 20 to 30 metres before they begin to tire."

10th Place:  Black mamba
Many people claim this snake has a top speed of 20 mph, but more reliable sources put the speed arond 7 mph, possibly up to 10.

http://news.nationalgeographic.com/news/2003/01/photogalleries/snakes/photo9.html

"Although a mamba is fast, it rarely is able to exceed a speed of 16 km/h" (< 10 mph)
http://mysite.mweb.co.za/residents/net12980/myths.html

article on measuring speed of animals and the sundry false claims by various studies
http://www.abc.net.au/science/k2/moments/gmis9911.htm .