It's been awhile since I've weighed in on this subject, which crops up fairly regularly...
I believe that animals will be resurrected and will join us in the new earth.
Why?
Well, there really isn't a lot of scripture to back it up, but I do have a couple of things.
One is the use of the word "nephesh" to describe both the animals and man. "Nephesh" being translated soul. Plants and trees are alive, but do not have souls. Animals do. Or better said, as someone around here has in their signature, "You are a soul, you have a body." Animals are souls too.
Secondly, the fact that animals were part of the salvation via baptism of the waters of the flood. This to me is the most compelling reason why I believe that animals will share in the resurrection. As it states in 1 Peter 3:19-22 "After being made alive, He went and made proclamation to the imprisoned spirits— to those who were disobedient long ago when God waited patiently in the days of Noah while the ark was being built. In it only a few people, eight in all, were saved through water, and this water symbolizes baptism that now saves you also—not the removal of dirt from the body but the pledge of a clear conscience toward God. It saves you by the resurrection of Jesus Christ, who has gone into heaven and is at God’s right hand—with angels, authorities and powers in submission to him. "
No, this doesn't refer to the animals being saved, but they were a part of God's salvation during the flood. He so very easily could have simply called forth more animals after the flood subsided, but He didn't. They had their place on the ark and the ark is clearly a type of God's salvation.
Thirdly, God created man to live forever. It was due to Adam's fall that man ceased to live forever. Animals were created to live forever as well. Until the fall, no animal died. All were created as vegetarians, nobody ate another animal. Even the lions, tigers and bears ate the plants and fruits that were good to eat.
Forth, an animal was the first sacrifice and therefore are considered innocent of sin. The first death was an animal which God killed in order to properly cover Adam and Eve's nakedness. This "covering" was the first sacrifice for sin. Animals remained the subsitute for our holy and innocent Lord up until His death on the cross, which fulfilled all sacrifices. If animals were sinful, they would not be able to be sacrifices. Since animals are without sin, then they should not remain dead.
That animals are part of the new earth is clear for Isaiah tells us that the animals will be restored to being vegetarians again "lion laying down with the kid, leopard with the lamb and a little child shall lead them"...paraphrased badly, but you all are familiar with this I'm sure. And, I believe that not only animals are part of the new world, Cleo, Miranda, Buzzy, Kitty-Kitty, and all the other critters will be resurrected as they were innocent of sin, and therefore should not remain dead, while I, riddled with sin and the cause of their death and the Lord's death should be alive.
Not that I'm going to argue the point with Jesus if Miranda and Cleo aren't waiting for me in my mansion, but this is why I believe what I believe.