Are you asking about Group round games? Or knock-out games?
It seems like many Sports Bar-type places are showing current the Group 1:45 AM games, either via satellite (with English-language commentary) or via the local license holder: GMM/Grammy with Thai commentary.
I noticed a huge new sports bar on Sukhumvit, ~ soi 9-ish, which has huge signs saying they are showing Euro 2012.
Maybe just Google "Sports Bars Bangkok" and grind through the links/websites?
Obviously a bit outside of the tourist areas the police enforcement of opening hours is lax.
And in the area between Siam Paragon and Siam Discovery there is a large tent in a beer garden type set-up, with a huge screen and signs say they are showing the games.