OTOH, I got stuck at the 2nd cd of FF9, back in the days. FF7 and FF8 are among my all-time favorites, but I din't like FF9 enough to bother finding what I had to do... I also found the card game much worse than FF8's triple triad.
My answer would be:
The PS3 version of NFS Hot Pursuit (with all the gold medals)
The "Extreme battle'' modes of Resident Evil 2 (ps1)
Battle City, starting from level 1 (8-bit nintendo)
pre 1995. quite a few. However, with sheer dedication I've managed to beat most games anyways.
One example is Dune 2. I beat it back in the day as Harkonnen, Ordos and Atreides. But I played it for funs a year or two ago and struggled a lot from level 4 and couldn't get past level 6. Perhaps I lacked the patience due to bad graphics and annoying controls. Or perhaps we've all just grown soft by games of today.
Nowadays, the only games I find unbeatable are the ones that suck so hard, it's just impossible to get through to the end.