if you're heavy, then running can damage your knees, ankles, hips and other joints. But if you're relatively lightweight or have good form, then the chances for injury are very small, and the impact actually makes your bones stronger, and strengthens the tendons and ligaments around your joints.
As has been said, try to run on softer surfaces whenever possible, and avoid concrete! Running on the road is actually much better than running on the sidealk, as the materials differ that much in hardness. Tracks, trails and grass are the best.
and yes, swimming will get you in better shape than running, but without the bone-building that comes from impact activities. Swimming is an all-over activity and really requires you to build muscle. I'm an all right runner, but I can't swim worth a damn. I get tired after two laps, so I know that the people who can swim 20 laps are in incredible shape.