So I posted about my pest dilemma on the About.com cats forum. I got some good responses. Some users suggested I put cucumber peels on the floor or create home-made roach traps. I'm not sure I'm ready to go that far yet since I have only seen one roach and traps seem designed to attract more roaches.
I got some good advice from a coworker, though. He said "I'd skip the exterminator altogether. The cats will take care of the bugs - no problem. I used to use roach traps in my place, but haven't seen a single bug since getting my cat over three years ago. Plus, it's fun for them."
I guess time will tell. 99% of the people in my apartment building already have dogs or cats and they are dealing with the same problems I am. I'll try to find out what they do.