What kind of exercise can burn as many calories as running?

Any!: It all depends on how long you do an exercise and at what intensity level. Walking, swimming, biking, yoga, etc. Are all great exercises. There are some good tables online which list average calories burned per hour and you can compare. Doing different exercises is a good way to get overall health.

Swimming: Swimming would probably be the best. Cross training and weight lifting can also contribute to more calorie burn.