Easily one of the best titles on the NES.
It starts out with Dr Wily making 8 evil robots to destroy Megaman, and Megaman sets out to destroy them. It isn't too much of an amazing story itself, but that could be redeemed by redeemed by everything else, and it doesn't let down there. Mega man 2 fixes all the problems from the first; There is now an easy mode for everywhere outside of japan and getting knocked into the spikes won't automatically kill you. There has also been some tweaks to the physics. In the water, Megaman will jump 2-and-a-half times the size of his normal jump, which will be used to bypass walls you won't be able to get over otherwise. The controls are nice and responsive, the music is top-notch, ranging (to what I think) up there with Super Mario Galaxy's and Sonic CD's soundtrack. The gameplay isn't too difficult, which allows for a more enjoyable experience, not forgetting it's fun as well. Nothing feels game-breaking (except for a certain boss,) which is good for any younger players.
You might run into the odd glitch or flaw, but that does not distract you from this epic game.