Wow, I'm so glad I'm with nearly everyone else on the hiding thing!! DH and I bought a kitten like five minutes after we moved in together, as we're both cat lovers. We didn't give a stuff that the real estate demanded no pets be kept on the property - every place we rented (and we ended up with two cats) had that stipulation but we always kept our cats clean and the place tidy, and our parents would take turns minding the cats overnight before an inspection (which was about every 6 months and/or upon vacating the premises at the end of the lease). We just never mentioned we had animals, then when we recieved notice of an upcoming inspection, we'd drop them (and food bowls/litter tray etc) off at my parents' or the in-laws' the night before, go home and give the place a good vaccuum to get rid of any extra cat hair, then as soon as the property manager left the next day we'd go around and pick them up!
As a PP said, kids do FAR more damage than cats, and dogs are the same (unless they chew things/dig holes, but those problems can be fixed/covered up, too), and DH and I happily paid exterminators out of our own pocket to fumigate for fleas upon the expiration of our lease (except for the second place we lived in, because when we moved in we discovered a serious roach infestation which the real estate agent NEVER got around to sorting out despite several notices from us requesting it be dealt with, so ner ner, have some fleas, buttheads!) so that the next tenants got no nasty surprises.

Seriously, I'd crawl through broken glass to keep my furbabies, no real estate agent on the face of the planet is going to stop me keeping my pets, I don't care what the lease contract says about 'no pets'. What they don't know won't keep them up at night Good luck!