Although the mavens at FanGraphs would know for sure, my anecdotal impression is that this MLB post-season has featured more extra inning games. The A's lost their wildcard game to the Royals in 12 innings, and since then the Royals have had multiple extra inning games against the Angels and Orioles. And the Giants and Nationals played an 18 inning classic last weekend.
The longest extra inning game at any level occurred in 1981, between Pawtucket and Rochester in the International League. That 33 inning affair had to be completed two months after it started, when it was called after 32 innings. Dan Barry's Bottom of the 33rd recounts this game in reverent detail. (One tiny detail that made me happy--the discovery that at the time the International League was headquartered in my hometown of Grove City, Ohio.)
Extra innings are just one more reminder of how baseball is different. As currently played pro basketball can never end in a tie, and pro football almost never can. But those games alter their rules in overtime, in ways designed to hasten the game to a decisive conclusion. And both basketball and football are ruled by clocks--shot clocks, play clocks, time out clocks, 2 minute warning clocks--throughout regulation play.
Baseball has no clock, ever. Extra innings proceed in the exact same fashion as the preceding nine innings. Theoretically every single game could go on forever. That is just fine with me.