As strange as it may sound, if a game is frustrating me I'm already at the point where I consider it worth completing, so I see it through.
I'm the kind of person that gets very upset about difficult and frustrated games, but I realize that as long as I'm not hurting anyone else and I'm not hurting myself, it's okay to get a little angry about it now and again.
I thought Godhand was difficult, and there were times I was EXTREMELY frustrated with that game, but looking back on it, Godhand is a game I'd instantly recommend to anyone. The same goes for games like Devil May Cry and Ninja Gaiden, cranked to the highest difficulty.
Hell, I beat God Of War II on Titan Mode, and that was the hardest and most frustrating thing I've ever done in a video game. I'll never do it AGAIN, mind you, but I saw it through and felt a personal sense of accomplishment out of it despite it being about a worthless thing like completing a video game.
I've been through real pain and enduring physical illness. There's not a lot I can do with the same degree of intensity I used to. Video games is one thing I CAN do with the same ability as when I was completely healthy, so getting angry about it is a way to stay tapped into the 'old' me, if that makes any sense.