I have quite a few options for when space has been an issue. We have a larger home now though and I've added some larger equipment. But I still use all of it. One is a simple step and hand weights and I will do some low impact step aerobics while watching TV. It takes just a few feet of space to step up and lift the weights. A little more to step up and kick.
I also have an Easy Strider from Wal*Mart. It fits in a closet when not in use. It's about $50. It stands about 1 foot high and is about 3' x 3' max. It's 2 pedals that you stand on and kinda stride/walk, with a battery operated calorie counter. My daughter got one similar that is a stair stepper. Same size, looks the same, but instead of a back and forth motion, the pedals go up and down.
Situps, pushups, squats, lunges, etc. All just take the space of your own body. And speaking of body...invest in a body ball.
As someone else mentioned, a mini trampoline is good too.
And then videos. You can have umpteen workouts by using videos. I prefer the WATP series. I've done them in tight spaces, like the few feet between my bed and dresser. I just turn sideways to do the sidesteps along the length of the bed, then turn back around to do the kicks.