I've had plenty of close matches.. a lot of games that ended with about 2 or 3 runs difference when I was simming the final overs, so didn't actually get to play through them unfortunately.
Closest one I played in was in one of my careers as a all round batter leg spin bowler. It was the finals for the one day Aussie season in my first year, I didn't even know it was the finals actually (they really need to draw more attention to this fact when you don't have the commentary sound on), was playing through the game. Came to the last over (once again, didn't even realise at the start that it was the final over), just bowled tight line and length, only went for the 1 run by the 4th ball. After I delivered the 5th ball I noticed that it was the last over, and that the score was tied with them on their 8th wicket. So, I freaked out a bit.. bowled my tightest ball I could, the batsman went to smash it past me and I managed to take a diving catch to get him out.
Nek-minit, trophey is being raised.. by the opposite team as they won on count back.. I thought I'd snared the win but instead I lost our team the trophey.
Also, on my pure batsman career, the first year T20 final was won on countback as well, didn't involve my team though, but I did think to look at the result.