In the post Zero Hour reboot continuity, he was Charles Foster Taine (Chuck for short) who was the Legion's resident architect and engineer. He has not received bouncing powers in this continuity and was only an honorary member of the Legion. As a maintenance man, he once built a specialty vehicle called the "Bouncing Boy" which acted as a bouncing juggernaut, smashing anything in its way.
He has yet to appear in the most recent reimagining, which began in 2004.
Recently a version of Bouncing Boy appeared in the Justice League/Justice Society crossover "The Lightning Saga" and the follow up story "Superman and the Legion of Super-Heroes". This one is supposed to be (roughly) the same as the original version.
Bouncing Boy is part of the core team in the Legion of Super-Heroes animated series, appearing Saturday mornings on The CW; he is voiced by Michael Cornacchia. In the series, Bouncing Boy is presented as an accepted member of the team, and the main pilot of the Legion Cruiser. In the episode "Timber Wolf," he and Brainiac Five quarrel over Bouncing Boy's piloting and engineering, but in the end, Bouncing Boy proves his abilities to his teammate.
In the episode "Lightning Storm", Bouncing Boy is seen working with potential Legion applicants, helping them prepare for the upcoming Legion auditions. In the same episode, his quick thinking helps him in the battle against the Lightspeed Vanguard. This led into the following episode, "Substitutes", in which Bouncing Boy gave encouragement to the future Legion of Substitute Heroes, where it was revealed that he himself tried out for the Legion four times before being accepted. In the end, he ends up coining the fledgeling group's name.
Ultimately, in the episode "Chain of Command", Bouncing Boy's quick thinking and observation allows him to form a plan that is crucial to the Legion's trying to save the inhabitants of the planet Winath. At the end of the episode, after Lightning Lad challenged Cosmic Boy for leadership of the Legion and prompted an election, an upset occurred - with the Legion instead electing Bouncing Boy to the position. After being elected Bouncing Boy receives a kiss from Triplicate Girl, in the end they are seen holding hands. He is seen taking an active leadership role in the 2-part episode "Sundown".
In the second season, his new position as leader is for the most part ignored, as Lightning Lad and Cosmic Boy are still arguing about it. It's possible that he felt responsible for Ferro Lad's sacrifice in "Sundown", and let Cosmic Boy have his position back. No canon explanation is given.