I mainly do all my squirrel hunting with airguns these days. My favorite is the Benjamin 392 .22 caliber air rifle. I've also used the Crosman RS2 with the .177 barrel (the .22 barrel just wasn't accurate enough no matter what type of pellet I tried). Last year I tried out the Crosman American Classic .177 pistol. It worked pretty well up close.
To answer your question about the biggest thing I've shot, probably possum or armadillo.