In my case, I've been stuck in plenty, but the most memorable of them was when I got stuck in a legaia 2 puzzle in which I had absolutely no idea what in the world I had to do for the longest of times. I ended up cheating on it and beating it and felt bad about that, but I just couldn't figure that puzzle out for the life of me. Kabel ruins was horridly difficult in puzzles >.<. I loved the game, but the puzzles in it were just so tough to  beat.

I don't know if this counts as a puzzle, but in Team Chaotix's Mystic Mansion, I got stuck for 6 years trying to find the target switch way above me to progress to blow out the torches. This was long before I even accessed the Internet myself, like at 10. I was 6 then.

If it doesn't count, try level 3 in the Pokemon Puzzle Collection demo for the mission category on the Pokemon Mini or the sliding puzzles on levels 2 or 3 of the same demo. 7 minutes of trial and error a few weeks ago and finally found how to solve it.

I remember being stuck at a puzzle game when I was younger. I played Pokemon Puzzle League from the Nintendo 64 and I wasn't exactly the best puzzle player. Worst of all, this game was timed so I had to do quick thinking on trying to beat my opponents which were the gym leaders, elite 4, and other people from the Pokemon anime during the first season. Hard mode made it really bad for me and I would get frustrated from playing it. Luckily, I am able to play that game a little better than what I used to. There's nothing like feeling accomplished!

Sayanos : I am not sure if this will count or not, but back in the days that I played Super Mario Galaxy, I could not seem to find one star that I needed. It was the hidden star of the deep Dark galaxy. It really took me like a year to find it. I finally was just swimming around at the bottom of the lake one day, when I saw an orange flash through the crack under one of the sunken ships! I instantly knew what it was. A Launch star! Next I had to figure out how to get under there. Around the ship, I could see mines. I tried shooting star bits at one to detonate them all at once, but it did not work. Upon inspection, I found a green shell. I threw that little baby and blew that ship clear off the launch star and was off to the Boo in the Box!

Plenty of times. A lot of PC games I had as a kid I never finished until I got much older.

I'd always get stuck at some part.

But the most recent one I could think of was on Skyrim. It was the "Pelagius hip bone" quest.

Of course, you can just try combinations with most of the basic ones, but this was different. It was just me falling for a trick for far too long.

I was somewhere in towards the end of Myst, and it had some really annoying parts. I generally lack patience for puzzle games nowadays. I used to play puzzle games like Adventure of Lolo and Tetris, but now just a simple fetch mission in borderlands had me grousing and grumbling.  
"I can't get up there! Why is it always somewhere out of reach? Who could have possibly left that there!" Blah blah blah

Firstly i am pretty embarrassed to state this but i will because i find it funny in retrospect. 

The puzzle if you could call it that, caused me the most grief was were you had to follow that guy in the 3D maze in The temple of Ancients in Final Fantasy 7.

Basically i was talking to a friend and did not see where he ran off to. Therefore i did not know where to go at all,. I spent perhaps an hour trying to find out where i was supposed to go and gave up, And this was a time before youtube videos could be found to help you. I am not even sure youtube was around at the time it was around 12 years ago. 

Either way i ended up playing through the whole game again just to see where this guy went.... So 20-30 hours wasted i suppose. 

So morals of this story are.. Do not let friends distract you too much, and never just use one save file for an RPG!