There are few games that remind me of the good ol' NES days more than Ninja Gaiden. I adore the first one. It's one of my all time favorites. I like the second and third, but they don't have the special meaning of the first for me, since I didn't play them as much when they were new.
The first one is tough as nails, but I've actually beaten it. Once. Ever since then, I play up to the final boss and get reminded what a pain it is to beat him, since dying takes you back three levels, and I quit. There's a trick to all the bosses in that game though, including the final one: That Jump 'n Slash special attack. If you can get it and hang onto it til you reach the boss, you can kill just about any boss in two hits. Jump into them with that special attack, and it'll drain their health. The final boss is still a pain though, because you don't have enough ammo for that special to take down all of his forms in one go. Luckily, once you beat one of his forms, you won't have to beat it again if he kills you. But you WILL have to play through the last three levels again.
Ninja Gaiden II NES is very good, especially with the cool wind and lightning effects. It's much easier than NG due to the shadow ninjas. Just get them to stop where you need to attack, like in the boss's weak spot, and slash away. As long as you don't move, they'll stay there and attack, and you won't take any damage when they get hit.
Ninja Gaiden III is a bitch for me. I've never beaten it. In fact, I've never gotten past the fourth stage without using save states. I know some people say it's the easiest of the three, but I find it ridiculously hard. Some of the levels are stupidly long without enough checkpoints, and they really throw a ton of enemies at you sometimes. Especially in that level with the static/white noise background. I usually play a few levels into it and quit out of frustration. The stupidly limited continues aren't even an issue, because I get pissed at the game long before I run out of continues.
I have the Lynx port of NGIII too. It's a very faithful port, but some of the sprites were enlarged without enlarging the hitboxes, so the hit detection is off. And the music was horribly butchered in the port. Other than that, it's fun to play...until the frustration factor kicks in.
I adored the NG Arcade game back in the day. My school had a roller skating day at the local roller rink, and they had a NG cab there. I used to play that game all the time, sometimes just to see the wicked Continue screen where a spinning blade descends toward Ryu, getting closer and closer until you put a new quarter in. There's also an abbreviated Lynx port of the arcade game. I've played the ROM, but haven't picked up the cartridge yet because it's pretty rare. Really an impressive port for the time.
I've barely played the new Ninja Gaiden games. I'm just not that interested, because the gameplay and story (from what I've heard) have nothing to do with the originals. I don't see how they can bear the same name when it's the only thing they have in common.