The hard part about this is that the animals have to be a star of the film. I'm guessing that you already are looking at the regular suspects, which are mostly cartoons (unless cartoons are disqualified). Also, some of these are fictitious animals:
Babe
Babe 2
Watership Down
Once Upon a Forest
Turner and Hooch
The Plague Dogs
The Beethoven Movies
The Secret of Nimh (and the abominable sequel)
The Neverending Story (and 2, and 3)
Labyrinth
Dragonheart
Teenage Mutant Ninja Turtles (and 2, and 3)
Every Which Way But Loose
C.H.O.M.P.S.
Man, that list can get long very fast.
Labyrinth and Watership Down are awesome, how dare you yadda yadda yadda.
Does Man's Best Friend (1993) count? The dog was sort-of on our side some of the time. :P