I remember when I was a kid, maybe 6 years old, my parents bought me Final Fantasy for NES. No matter what I did, I couldn't beat Garland (the first boss! Lol) for the life of me.
I picked it up a few years later and beat him on the first try. And then went on to beat the game a week or 2 later and this begun my love for RPG's
The only game I have not been able to beat was Attack of the Killer Tomatoes. I would get to the evil lab and never get passed it.
Other than that, instead of not being able to beat games, I just get extremely tired of games before I beat them and end up quit playing them. (The last remnant, final fantasy 10,12.. Final fantasy 13 just blew major balls and I can't beleive I spent $60 on it.)