Just dabbled on NES a bit, I played
Kung Fu. Also known as Kung Fu Master, it is a port of an arcade game in which Thomas must rescue Sylvia from Mr. X on the fifth floor of his dojo. I had this game as a kid back in 1994, the first time I had the NES. It's an early beat-em-up game-- enemies attack from both front and back as you proceed through each floor and face its boss. Floors 1, 3, and 5 progress from right to left, while 2 and 4 go left-to-right. A to punch, B to kick. Enemies (other than bosses) are worth more points when defeated by punch, as it has a shorter range. Bonus points are rewarded at the end of each floor for health and time remaining.
When you rescue Sylvia, the game starts over and the difficulty increases. A "dragon" icon keeps count of how many times you've finished the game on your current "credit".
For the record, I completed two playthroughs on "A" difficulty (pretty sure it changes to B after saving Sylvia once) and then died to the Giant (boss of the third floor) on my third run through the game. My score was 391,100, which is easily my personal best now-- I had never completed the game twice in a row before, though I never really took time to get good at it... certainly there are players out there who have really practiced and are able to get a score in the millions, with dozens of consecutive successful Sylvia rescues on one credit. (
EDIT: Looks like the WR is right around 3 million.) I don't remember earlier PRs, but they were in the 200K range.
IMO the fourth floor is the most difficult, especially on B difficulty, although the flying insects are easy enough to avoid (and you can kick them to death), you've got to deal with that dwarf wizard boss and his deadly fireball attack... and in hard mode, you often get knife throwers coming from behind on top of that.

A knife thrower can show up during any boss fight in B mode, actually, but because this wizard is already the hardest boss in the game, prepare to lose a lot of lives at this specific spot. (and if you got careless and hit some bugs on the way there, you can
really kiss your ass goodbye.) I lost three of my four lives there during the second run. (There's only
one extra life, which you get at 50,000 points, usually at the end of the second floor during the first run)
I've played a few other arcade-style NES games, like Pinball, Mario Bros., and Mach Rider but I do not remember my high scores. In Pinball, the flippers become invisible when you hit 100K...
EDIT: Just played a game of Mario Bros. I sucked. My score was 204,210, for what it's worth, and I game-overed on just the 24th phase. I have to get better at controlling Mario, just takes practice. (although two of my deaths were from fireballs spawning right in front of my face) It's a lot more slippery in the original NES game than on the GBA remakes, where I maxed out the score fairly easily. Also, as in the case of Kung Fu, there only seems to be one extra life. But hey, nothing says old-school-gaming-challenge like trying to get a good old high score on one of these classic arcade titles...