What physical activities besides weight lifting help build muscle?Already I see some great answers. First off, I would recommend picking up a sport or two if you have the time. I, for one, play a lot of soccer; mostly because I hate pure running, but also because I really enjoy soccer. There are a few problems with sports if you're trying to build muscle, though:
1) Sports in general (unless you're talking something like wrestling) tend to favor one side over the other. I.e. I'm right footed, so I shoot and kick mostly with my right foot. I can kick left footed, but most of the time I can't get the right placement on the ball and any given left footed shot is going to be weaker than a right footed shot. Consequently, I do my best to switch to my right side. This means that I'm subtly building up the muscles in my right leg more than in my left leg. It's not terribly obvious, especially if you try to mix in both legs, but it's an issue with most sports.
2) Athletes in any sport train with weights to get stronger. If you want to gain muscle mass, just playing basketball or baseball won't build much. It will get you good cardio, but not much muscle mass.
3) Most sports focus on particular regions. Baseball and basketball: arms and upper body. Soccer: lower body. Since I'm assuming your time is limited I'm going to assume that you don't have the time to play both soccer and basketball every week. Rather, use the sports as a way to improve your cardio; muscle mass will accrue, but not necessarily in the way you want it.
I'm not saying that you shouldn't play sports, just that sports aren't necessarily the best way to build muscle. Great cardio, but not much for building muscle.
Another idea was to add weights to your current exercises - leg weights, carrying dumbbells when you jog, etc. That certainly is a good way to build up some muscle. The problem with this, just as with picking a single sport, is that you have to add weights to every movement you make or you'll end up with the same problem as with sports: overbuilding in certain body areas and under-building in others.
However, the idea behind this is the most sound: the best way to build muscle is to add weights to any movement you normally make. This is why gyms have so many different machines and types of weights available.
My personal recommendation is surfing. You never know how the waves are going to be until you get there, meaning you get variable resistance with each session. On top of this, like swimming, you need your entire body to paddle out and then to stand up and control the board. One issue with surfing, though, is that you can end up overworking your shoulders, leading to impingement. The best way to avoid this, as with any exercise, is to stretch adequately before you begin.
If you don't live near water, you can do what I do: On my longer runs, I stop at every cross street and mix in a set of either 1) push-ups, 2) pull-ups, 3) crunches, etc. This way, your muscles are already tired from the run and then you blast them with a variety of exercises. You have to be confident in your ability to make it back home, though: doing push-ups at every stop light can really take the air out of you. You're also going to want to make sure that you're taking in enough protein to make any exercises you're doing worthwhile.