I like the question.
Contra
Journey To Silius
Final Fantasy IV (different versions)
Illusion Of Gaia
Chrono Trigger
Honorable mention: Robotrek
These are the games that come to my mind. Maybe there's a couples of titles on the NES that I've beat a couple more times as I discovered them as a kid like maybe Double Dragon II with my cousins, SMB3 or Mega Man 2 because we had only a few games to abuse, but I decided to answer the question with games that I consciously wanted to play all over again. I usually don't play twice RPGs even thought I LOVE THE GENRE so that makes choices 3,4,5 more significative for me. In the last 2 years, I played and completed Journey to Silius 3x on the top on the couple of times as a teen and for Contra, I beat it since the '90 with 1 or 2 Players and I lost count. I decided to stop playing it until I play more of Super C and other games of course... Next time I want to beat it 2 Players with a girlfriend ! Never had a gamer girlfriend, thought.
I know it's more that you ask for, but you gonna get use to it because that's my style.