If I had a Gorilla by Mercer Mayer.
He also has a great website in case you need a funny moment or two. (Comes in handy if you happen to get a nasty cough and have trouble with the read alouds!)
I Wanna Iguana by Karen Kaufman Orfoff, illustrated by David Catrow
This is an adorable tale of Alex and his mother debating the issue of a pet iguana.
Had to read Hi! Fly Guy by Tedd Arnold. Doesn't everyone have a pet fly?
Other great pet stories are:
The Berenstain Bears' Trouble With Pets by Stan and Jan Berenstain
Dino Pets by Lynn Plourde
Daniel's Pet by Alma Flor Ada, illustrated by Brian Karas
Pinky and Rex and the Just Right Pet by James Howe, illustrated by Melissa Sweet
Author's Pet Business by Marc Brown
The Perfect Pet by Margie Palatini, illustrated by Bruce Whatley
Pet Show! by Ezra Jack Keats
Henry and Mudge books by Cynthia Rylant
I'm going home to read. What else can I do in the rain?