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Some games are good to keep track of scores in.
Where it is difficult to get a 1-up loop or continue keeping score is best. If there are time constraints.
original Castlevania might be good for that. Although it's very hard to beat it without continuing. There are hidden items for score.
Super Mario Bros. was fun for score until discovering the 8-2 1-up loop. Then it's disqualified. They took the 1-up loop out of the arcade Vs. Super Mario Bros. which helped.
Zanac may have some backwards warps but it's hard to find. I think it's suitable for score. I'm still keeping track of scores I had with that one for years and years.
Donkey Kong is good. I still wonder how people can actually get to the kill screen without cheating.
Touhou seems excellent. I still need to be survivable, not ending the game seems to be leading to higher scores.
Several Atari 2600 and arcade titles are meant for this. Centipede comes to mind. Pac-Man and Ms. Pac-Man are great. Berzerk too.
An alternative for games without decent scoring is to play for time. The speed runners are insane, they play a different game than I do.