Mega Man 2 (1989)
I played Mega Man 2 after I played Mega Man 3. I got it by borrowing it in exchange for my Mega Man 3. I never saw Mega Man 3 again, which wasn't a big deal since I played it to death.
Mega Man 2 definitely wasn't as polished as MM3. It wasn't as long, and wasn't as deep, but I think the playability is much better. The levels are fun and the music is kicking. The most memorable stage for me was Clash Man/Crash Man (still don't know what it's supposed to be - neither really describe his power). This theme, and the opening sequence really got you motivated to be a robot and save the world. It also had the best Engrish. I mean, seriously, even within the game, the names aren't consistent.
But Mega Man 2 is fun stuff. It highly improves on the first game (which I never played till I got an emulator) and fills it with all the things that make Japan great. The levels are challenging, but fun. The weapons and items are varied and fun. The characters and plot are fun. Basically, the game is fun. Mega Man 2 and Mega Man 3 are the best games in the classic series, but they're like apples and oranges. And both made me fall in love with the little blue bomber.
Mega Man 2 is missing the storyline aspect that Mega Man 3 had. Every Mega Man has the same plot, but this one had a decent boss battle. Of course, you fight a Dr. Wily robot first. Then you descend into a cavern where you find out Dr. Wily is *gasp* an alien. He dips and weaves, trying to get you, while stars fly in the background. But something's not right here. The stars are going, but you're standing still. The alien is moving very methodically, and it doesn't meld with Wily's style of giant robot warships. Lo and behold, when you fill that alien full of Bubble Lead, the lights come on, and you are standing in a holographic chamber, with the real Dr. Wily at the wheel.
Then we see Mega Man walking, while a picture of a village changes seasons. What's going on here? I don't know. Doesn't seem to have to do with the plot. It's pretty (although Mega Man's face looks like he just sucked on a lemon). Wikipedia says he took a long walk home to think about his decision to spare Wily, but that's not evident on the screen (this would later become a much more pivotal point in Mega Man 7, when it seems Mega Man is about ready to break the first law). Then there's credits and the world's okay. Well, can't expect much from a game from 1989, but without it, a great legacy would never have been born.
This game and Mega Man 3 laid the foundation for the Mega Man section of Gatecrash. Much of the style comes from this game, but many of the plot points come from Mega Man 7. I think without this game, I would not have been as interested in Gatecrash.