For me, they're
Golden Sun: The Lost Age I started playing this in 2002, but I got stuck in the desert area at the beginning of the game; consequently, I didn't finish it until 2005 when I somehow figured out where to go. This game was much longer than the original as well, so, even after figuring out how to get past my block, it took me a while to beat it.
Golden Sun: Dark Dawn I bought this game in 2012 because I saw it at a Target when I was out of town. I think I'd heard about it briefly but never saw it in stores. I proceeded to buy it and play it for about thirty minutes. I picked it up again in 2014 and played it for a few days on another road trip. I can't remember if I played it again after that, but I got stuck. A few days ago, I picked it up and somehow immediately figured out where to go (funny how that works). Maybe I'll beat it some day.
Star Tropics I'll probably never beat this one. I've been starting a new save file, beating the first cave, putting the game down and forgetting where I was, and starting a new save file every few years since 1998. My brother had beaten it a few years earlier but I don't think we actually owned a copy until '98. I'd really like to play through this one in its entirety, but I can't seem to stick with it.
Metroid Prime 3: Corruption The original Metroid Prime is my favorite game of all time. I was not a big fan of the second one. The third one is cool, but I hate the Wii Remote controls (I've heard of a Dolphin version that uses mouse and keyboard, which sounds awesome); they just aren't conducive to long game sessions, which Metroid Prime requires. This is another one that I've restarted multiple times because I forget where I was, but I became so tired of replaying the first hour or two that I've just decided to be lost if I ever get back to it. So far, I've been playing this since 2007 on and off and have never beaten it.
Bomberman 64: The Second Attack For some reason, I thought this game was really hard back in the day. I recently started over and beat it over the course of a few weekends with a friend. It was difficult, but not as hard as I had remembered. So this one spanned 2000 to 2020 (I can't remember if we finished it early this year or late last year).
I'm sure there are others, but some games I would probably consider "abandoned" because I don't intend on ever finishing them (like the Banjo Kazookie games).