Maybe it's a little embarrassing, but I totally did! When I was little, I ALWAYS wanted a kitten, but my dad is really allergic to animal fur, so having a cat was always out of the question. I think I was around five or six, and I created an imaginary kitten for myself so I could at least pretend to have the cat I wanted. It was a little tabby cat named Kina, and I'd always leave little play dishes out for it so it could 'eat' and 'drink'. I'd take it on walks (in my play stroller, of course), dress it up, the whole nine yards!
Of course, I grew out of the imaginary friend phase, but I think that should've proven to my parents that I was at least ready to take care of some sort of pet. :P I might see if I can get a fish over break. They're pretty low maintenance AND they're pretty to look at!