Shin Megami Tensei: Nocturne still collects dust to this day. I want to play it and complete it, but after having my later game data deleted, and with all these games I'm currently playing, I can't convince myself to pick it back up.
Final Fantasy V, which is the only game in the mainline series I haven't beaten. That will be rectified in a couple days though, because I'm playing it right now!
I'm also ashamed that I haven't beaten Battletoads yet. I can get to the next-to-last stage, but the weird orb thing always catches me. Probably because I'm playing on an emulator and not an actual console.
Not quite ashamed but have to say SMB Lost Levels japanese version.I can beat SMB NA version start to finish without dying at all. But Lost Levels whoops my Ass and Game Over music taunts me to no end.
You should do the one-up trick with the turtle at the very beginning of stage 1-1. That's pretty much how everybody gets through it. Here, watch this:
Suikoden IV. It was the first one I played but I went through it without ever sharpening my weapons because I didn't know what the blacksmith was for. Stuck on the last boss and can't beat it at all because of low damage. Will replay it again one day if there's no HD collection eventually.