-Classic Mega Man
-Mega Man X
-Mega Man Zero
-Mega Man ZX
-Mega Man Legends
-Mega Man Battle Network
-Mega Man Star Force
I'm a fan of every series I've played so far. Haven't played X7-8, Zero 3-4, ZX, and Star Force. I can't remember which game I played first; Legends 2, or Mega Man 5, but I got into the series many years later.
My favorite series is the Classic one, but depending on my mood, I might prefer the X series instead. My favorite game from the Classic series would be 9. Some good bosses, great weapons, cool platforming and stage gimmicks, and good difficulty. At first I liked 10 better, but that was because 9 was so hard for me the first time I tried it, to the point I considered it cheap. But after giving it another try, I realized that once you get the hang of it, the game has a great flow.
Haven't played Zero 1-2 enough times to have a solid opinion about them, but I remember having trouble with Zero 1 because of its lives system. I had fun with Zero 2, though.
The Legends games are good if you want to chill and play a simple game. Everyone talks about how bad Legends 1's controls were, but I got used to them when I got to Kattlelox Island for the first time (and, if you read everything I said up until this point, you'd know that I played Legends 2 before playing Legends 1). If they ever make Legends 3, I only ask that they fix two issues I have with both games: Give Volnutt the ability to use more than 1 sub-weapon at a time (this is Mega Man, after all! One thing I like about the series in general is how you can experiment with the weapons, but in a game where you can only use one at a time... It kinda kills the incentive to test them all, especially if you find one you find comfortable using for the rest of the game).
Also, make better enemies/bosses. Anyone who played the games knows that most enemies and bosses can be trivialized by circle-strafing.
As for the BN series, I like them because, to me, its battle system is unique. Never played a game like it. Coming up with certain combinations of chips that can destroy a boss in less than 30 seconds (or 10 seconds, if you're good enough) can be fun. Sure, it can get stale after a while, but fortunately there are a number of ways to do that, instead of just a single chip combination being able to pull that off.