So, when I first started reading this thread, the first film that came to mind was
"Milo & Otis". That film has scarred me for life...in that every time I think about it, I get depressed and teary eyed.

BAH!
And YAY for whoever mentioned
"All Dogs Go To Heaven"!! That one is depressing too!!

As is
"The Fox And The Hound". What the hell is up with all the depressing ones??
Uhhh, let's see:
"Finding Nemo" (WIN - hands down)
"The Lion King"
"Homeward Bound"
"Free Willy" (I was obsessed with this movie ... some people think I named my cat after the whale XD)
"101 Dalmations"
"Beethoven"
"The Aristocats"
"Lady And The Tramp"
"Babe" (OHH yeah -- EPIC)
"Black Beauty"
"Charlotte's Web" (Not the recent one ...)
"Chicken Run"
"Happy Feet" (Dancing and singing penguins FTW!)
"March Of The Penguins"
"Hidalgo" (Yes, I'm counting this as an animal movie ... horses OWN)
"Iron Will" (Haven't seen this one in ages, but I love it!)
"Ice Age"
"The Jungle Book" (Animated AND live action versions -- YAY!)
"Jurassic Park" (And the other films...

)
"Land Before Time" (Because dinosaurs ARE animals too!)
"King Kong" (I never considered this an "animal" movie ...

)
"Madagascar"
"The Rescuers" AND
"The Rescuers Down Under"
"Seabiscuit" (Again, HORSES RULE!)
"Stuart Little"
"Whale Rider"