Any shmup game, I am horrible at them but I can't help but to enjoy them for their general insanity.

I suck at platformers like that too. Just today I tried Mari0 (that's Super Mario with the portal gun) and I was almost ashamed of how much I failed :D

And I never got past the third boss in Super Meat Boy, even though I liked the game and wanted to get further. I even had to lower the difficulty in the last level of the first Trine. I guess I'm not entirely hopeless, there are some 2D platformers I won in recent years, but there are many more I had to play on easy (which almost doesn't count) or just got frustrated and bored with. I even had to give up on the final fight in Unepic, even though I really loved that game. I shudder to think how many hours I wasted on that level. Makes me wonder how I ever beat Aladdin or Prehistorik when I was a kid.

A lot of them ARE unfair. Often the right solution makes less than no sense. One could waste hours trying to figure it out and still fail. It's not as bad now as it was back in the day (not that the games were bad, just bat shit insane), but even the best adventure games I've played, that were for the most part logical and sensible had a few puzzles that just were impossible to figure out, unless You already knew the answer. I guess it's just really hard to make good puzzles, because when you are making them, You do know the answer, and it all makes sense to you.

It depends on ones perspective of suckness. It also depends on with whom you're comparing yourself.

I probably thought I sucked at some games after playing them superficially. If I really like some game I do try to get better in it, either by practice or by reading some manuals, forum tips and similar.
Before Civilization 5 I thought I sucked at Civ4 and especially in Civ3. After I became really good in Civ5 I decided to go back to Civ3 a little (currently at 60 hours and it looks like victory is very close) and I found out I don't suck anymore, except in combat, but it's just an awful system so it's ok to suck at it. B-)
I used to be an average Counter-Strike player, but if I would play it now with someone who invested some time in it, I'd probably suck big time and maybe killed someone by accident. XD

Currently my one is Eador. I love it but I still suck at it even on beginner.

Point and click mystery/adventure games. I absolutely suck at them. But I love them, they are my favorite. I have a hard time finding things and figuring out how to put them together. I really do. I mean how am I supposed to know that the only way to open a specific locked door is

1. go the beach and collect a specific patch of clay,
2. pick the pocket of the waiter to get the key,
3. press the key in the clay, AND put the key back in the waiter's pocket.
4. fire the clay in the fireplace in my room
5. find 5 pieces of scrap metal and sneak into the smithy when he isn't there to smelt it. 6.1 don't forget the fireproof gloves from the kitchen (even though the smithy should have something I could use)
6. then pour the hot metal into the fired clay mold.
7. cool it in the water and THEN I can use it to get into the locked room?

How? Especially when I've got two bobby pins in my inventory? But the bobby pins are supposed to be a gift to a waitress whose hair fell out of a bun or some such thing.

Why do I like those games? I have no idea but they draw me in every time. lol