I don't have a gift closet. But I do have a gift bin. It's a large rubbermaid box with a lid. I buy sale stuff to keep in it. Right now it's mostly kid stuff, Barbies, Bionicles, Funky colored nail polishes, sports stuff, stuff like that. My kids are notorious for telling me the day of when they are invited to b-day parties and things like that. I started keeping the bin when my son was in Kindergarten. The bin has saved my booty more than once. I just tell the kids to go pick something out of the bin and put it in a gift bag.
I don't keep much stuff for grown ups in it. I guess I should probably start.