He started liking the broom when he was our truck kitty, and we had to get an extra broom so we'd have a clean one (we used the old one to sweep the floor, silly us!).
Abby loves to be brushed. Chynna loves to be brushed and vacuumed. I recently got a Dyson Animal vacuum with a turbine furniture tool. Basically it's a mini power head with a rotating brush for furniture. One day while I was vacuuming Chynna kept putting herself in the way of the vacuum demanding that I stop and vacuum her. I tried the turbine head and she absolutely loved it!
She's the first cat I've ever had that isn't afraid of the vacuum cleaner monster.