When I first saw Angry Birds, my first thought was that it copied (or more diplomatically, “was inspired by”) another game I had played called Crush the Castle. I looked up some details, and discovered that Angry Birds was released on December 10, 2009 while Crush the Castle was available in early 2009, at the exact time Angry Birds started their development. I will say this: Angry Birds added a lot more personality to the game. I thought it was interesting that Angry Birds kept the monarchy/military theme for the enemies, with pigs dressed in crowns and helmets. Angry Birds also uses a slingshot rather than a trebuchet.
And here Crush The Castle (jump ahead to 30 seconds):
Link: Crush the Castle
Also, as a side note, the game “Osmos” which is included in the Humble Indie Bundle is also reminiscent of a flash game I played years ago as well. I couldn’t find the old flash game, but it involved controlling a fish to eat smaller fish while avoiding larger ones. Each time you ate a smaller fish, you’d become slightly larger. It was the same basic gameplay as Osmos, though Osmos seems to have added a few more features.