Here's an obligatory video featuring the various executions found in the Gears of War 3 beta.
I figure many of you haven't seen some of these moves, since it's not often you get the chance to initiate them without the opposing team taking notice. I will say, though, that people are getting better and better at saving the super long ones (e.g, the face-punching execution) for the final kill of the match.
And when you happen to be the final kill of the match, it's the worst thing ever.
My personal favorite shown here is the one where you pull a dude's arm off and pummel him with it. Kind of can't believe I wrote that sentence. Games sure can be remarkably over the top when they want to.