Spartan and I are usually pretty good at powering through even the crappiest, hardest co-op games. But, there are two co-op games we gave up on and I don't believe we were even on the hardest difficulty on either one.
Game 1: Perfect Dark Zero. I'm pretty sure we weren't even playing the hardest difficulty, we were playing the second hardest (Perfect Agent IIRC). The checkpoints were ridiculous, the AI was extremely smart, and our weapons were terrible. I think we got to level 12 or 13 on this difficulty (out of 14) and quit. Never going back, but I'll never forget how terrible this was.
Game 2: Command & Conquer 4. We'd played C&C games for years but this one was impossible. There were parts of C&C: Red Alert 3 that were frustrating and near impossible, but we got about 2 or 3 levels into C&C4 and quit. Not only were the missions hard, but I think the gameplay itself was rough and different than other C&C games. I'd like to try this again someday (especially since I don't think there have been any C&C games since), but I'd have to be pretty bored haha.
Anyone else come across games you'd consider "unbeatable", or at least unbeatable in their harder difficulties?