Calvin has been seen using balloons on a few occasions.
Usually Calvin fills balloons with water to use as Water balloons to throw at Susie or at Hobbes for a practical joke. Calvin and Hobbes often use water balloons as part of their G.R.O.S.S. club to get rid of Susie (by throwing them at her).
One instance of use of balloons was a Story arc in which a conventional helium balloon was somehow able to lift Calvin high into the sky (this was possibly an event that took place in his imagination). The balloon went thousands of feet into the sky, then popped when the air pressure in the sky dropped too low. As he was falling, Calvin managed to save himself with his Transmogrifier Gun by transforming himself into a light particle and zipping back home. It was suggested that Calvin flew over Chagrin Falls, Ohio (Bill Watterson's hometown) due to numerous hints Calvin gives (as well as the scenery).
There are also many regular strips with balloons, such as when Calvin began to blow a balloon, and his head inflated instead of the balloon. In another early strip, Calvin was seen with another helium balloon. He climbed with it onto a stepladder (which Hobbes was holding for him) expecting it to lift him up into the air. To his disappointment, nothing happened, to which Hobbes suggested jumping. Calvin did this, but only for him to land flat on his face while the balloon lifted up without him.