Heavy punching bags provide a cardio workout, resistance training and a means for developing good form in your punches and kicks. However, they can be tough to install and may be inappropriate entirely in some living or training situations. If you're in such a fix, you're not out of luck. There are other ways to get the same benefits.
A free standing punching bag looks and acts much like a regular punching bag. It's cylindrical, padded, and offers the same amount of resistance. However, these bags don't hang from the ceiling. Instead, the cylinder sits on a reservoir you can fill with water, stones or sand. This provides a counterweight to keep you from knocking it over with your strikes. In general, you'll use this kind of bag almost exactly as you would a regular heavy punching bag.
Called a "muk-yan-chong" in the traditional Chinese, this piece of training equipment consists of a wooden striking surface with wooden arms and legs to practice trapping, positioning, and blocking. This is an expensive option, costing as much at five times the price of a heavy punching bag, but is more flexible as a training tool --- and you don't have to mess up your ceiling putting it in place.
If you work with a partner, you can get everything a heavy punching bag workout would provide and more by working with a kick shield. These foam pads have handles like a medieval knight's shield. One person holds it while the other punches and kicks it. Some advantages of a kick shield include a wider variety of appropriate strikes, greater mobility, and a surface that's friendlier to your knuckles. The disadvantage is you can't use one if you don't have a training partner.
If you have a camping pad and some rope, you can tie it to a tree and use it the same way you would a heavy bag. For direct punching workouts, you can simply use sofa cushions, or the top half of an easy chair. Any thick, padded surface with some stability beneath or underneath can work as a heavy-bag replacement if you apply a little ingenuity. Although none of these options are as suitable as a premanufactured training tool, they're better than not training at all.