I've got a Eureka Boss Lite Cordless that works well for crap the dogs drag in, little bits of paper from the shredder, etc. It certainly can't substitute when a good vacuuming is called for, but it is great for little in-between cleanups. Kind of like a dustbuster with a long handle.
I keep it hanging on the inside of the basement door, charging all the time so it's ready to go when needed. I'd never drag out a vacuum with a cord, so the cordless is nice.