I have been playing the first Ninja Gaiden on the NES because I heard so many good things about it.  While it seems to be a good game, there are some elements in it that makes me question its greatness.  If anyone used to play the game, can you tell me what makes it so great?

It was one of the first games that had "cinematic". It also has great music and fast paced gameplay and is very challenging.
In which level you are?

For its time it was a really fun platformer, had great cutscenes, and was hard as nails. NG3 is the best in the series, obviously. Its hard to play this game now a days cause Ryu cant climb the walls that he sticks to like you can in 2 or 3.

I see. Maybe I am too critical. The enemies re-spawning if the screen moves an inch backwards is really annoying however.

the MUSIC, the fast gameplay (its the fastest of all 3 NG's), the difficulty, the cinemas.

Lol, yeah, that was pretty common on the Nes games. In the same way some enemies "disappear" and you can take advantage of it. Specially on level 6-2 if I remember correctly.

I like the game so much, I still play it from time to time.

It was bad-ass playing as a ninja and kicking ass. I remember it as one of the first games where I experienced getting through certain sections and thinking I just kicked some major ass. Also, it was hard as hell and when you beat it you feel you've actually accomplished something, until you tell your mom and she says so what and that you've been playing to long and have to go play outside. Damn sunshine.