Football (soccer), but instead of a goal net there is a circular, quidditch-esque hoop high in the air (15- 20 feet up, maybe), and the goalie crease is a trampoline that only the goalkeeper is allowed to use.
Played on roller blades, with a tennis ball, on a football-field-sized clay court. Each team has 3 racketeers (they carry tennis rackets), 2 sticklers (they carry hockey sticks), and 1 Lone Gunslinger (he/she carries a hockey stick, but also has a tennis racket slung over his/her shoulder, to unholster and re-holster at will). The goal can be either a soccer net with a goalkeeper, or a raised hoop with no keeper.
Basketball, played on a hockey-sized court (2.1 times longer and 1.7 wider than an NBA court), with hockey-style line changes (‘on the fly’, rather than during stoppages of play), three 20-minute periods per game, first-basket-wins overtime, only 1 timeout per team per game, boards instead of out-of-bounds, and, instead of free throws, a 2 minute penalty kill following every 3 fouls by a single player. All baskets are worth one point only.
Baseball, but with more running and fielding plays, fewer shallow home runs, and quite possibly shorter (but not much shorter) games. In Inside-the-Park Baseball, there is a large, slanted outfield wall placed between the outfield and the outfield stands. The slanted wall – slanted, say, at an angle of 45 degrees – will eliminate shallow out-of-the-park home runs; shallow home run balls will instead bounce up off the angled outfield wall and back into play, creating a huge increase in triples, inside-the-park-home-runs, and throw outs. The size of outfields will remain the same as in conventional baseball.
Conventional baseball parks can be easily converted into an Inside-the-Park Baseball field: you just put a slanted wall over outfield bullpens and/or over the lowest outfield seats.
Ice hockey on a massive lake or in a football stadium. Instead of goalie nets, each side has a metal pole players have to shoot the puck at. Each pole is surrounded by a fairly large goal crease which noone on either team is allowed to enter. The ice quality is maintained by robo-zambonis