Interesting topic. I'm like Birdman; so far nothing has been so rage-inducing that I wanted to break anything, but I did experience frustration. Off the top of my head (I won't count Kaizo experiences):
-KH1. Just last year, I think. This was the time when I wanted to actually do challenge runs, so I decided to give a low level run a try (Lv 1 runs aren't a thing in the PS2 version). The run was quite challenging as expected (not having Guard for most fights is annoying), but nothing I couldn't handle.
Fast-forward a bit, I'm now facing the game's super-bosses (except Sephiroth). They were tough, but I wanted to push myself even further, because I knew I'd need that experience if I wanted to enjoy Action games anyway, so I tried beating Kurt Zisa without getting hit at all. This was literally the first time in my life (again, not counting Kaizo experiences) when I got stuck at a boss or whatever else for more than 40+ tries. Not to mention the 1-minute load times... but I wanted to beat it. I got to the point where I could dodge his vertical spinning attack 7 times out of 10 (his most dangerous attack, very little room for error since KH1's dodge roll barely has any i-frames at all), but I messed up dodging one of those purple spheres that come out from the sand (by far the easiest attack to dodge in his entire arsenal, imo). But what hurt me the most wasn't the fact that I did such an amateur mistake in the first place, it was the fact that I just had him. One more Gravity spell, and GG Kurt Zisa. But nooooo, I just had to mess up that one attack. Of course.
Fortunately, I was able to complete the challenge. Beat him at Lv 41, no damage. So I guess it was worth it.
-Not sure if this counts, but I'm going to bring up a fangame. Mega Man Unlimited. Particularly, its Endurance Attack mode.
Well, this was the second time I've gotten stuck in anything for more than 40+ tries. You have to beat 70 stages in a row, and if you fail, you've got to do it all over again from the beginning. Every time I reached stage 59-60, I was already at the 50-minute mark. And I couldn't get past those stage for the longest time (and when I did, it was only an one stage improvement per run. Beat stage 60, fail, there goes a 50 minute run. A couple more fails, beat stage 61, fail, there goes another 50 minute run). Man, losing a 50-minute long run so many times is certainly discouraging, to put it lightly. Enemies in the later stages hit like a truck, some stages had spikes placed everywhere, so you had to have near-perfect precision in your jumps, or it was all over.
But since I'm very stubborn and refused to give up, I actually completed that as well. I think I succeeded on my 60th try. I dunno, I lost count from 40 onwards. I think the dev posted about the outcome on his twitter.