This question is one that comes up time and again, especially with teenage animal-lovers around. This answer from Peter Kreeft's Everything You Ever Wanted to Know About Heaven makes sense to me. He doesn't look at it from the "immortal soul" angle that usually is raised, but from the promise of a "new earth" that is made in the book of Revelation.
The simplest answer is: Why not? ... Much more reasonable is C.S. Lewis' speculation that we will be "between the angels who are our elder brothers and the beasts who are our jesters, servants, and playfellows" (That Hideous Strength). Scripture seems to confirm this: "thy judgments are like the great deep; man and beast thou savest, O Lord" (Psalm 36:6). Animals belong in the "new earth" (Revelation 21:1) as much as trees.
C.S. Lewis supposes that animals are saved "in" their masters, as part of their extended family (The Problem of Pain). Only tamed animals would be saved in this way. It would seem more likely that wild animals are in Heaven too, since wildness, otherness, not-mine-ness, is a proper pleasure for us. The very fact that the seagull takes no notice of me when it utters its remote, lonely call is part of its glory.
Would the same animals be in Heaven as on earth? "Is my dead cat in Heaven?" Again, why not? ... Though the blessed have better things to do than play with pets, the better does not exclude the lesser. We were meant from the beginning to have stewardship over the animals (Genesis 1:28); we have not fulfilled that divine plan yet on earth; therefore it seems likely that the right relationship with animals will be part of Heaven: proper "petship". And what better place to begin than with already petted pets?
UPDATE: There is a discussion going on over this at Catholic and Enjoying It where, interestingly enough, Mark Shea posed exactly the same question. Its worth taking a look at if you're interested in the subject.