Defeat all the robot masters or mavericks in any or all of the games, without sing special weapons, just the plasma cannon/Mega Buster.
When fighting either version of Bass in Dr. Wily's castle in MM7, hit him at least once wil every type of weapon Mega Man has, including the Mega Buster and Rush Rocket Punch. Try this agaibst bosses in other games, too.
Defeat as many bosses as possible with the Street Fighter moves in MMX and MMX2. Some bosses, like the basic MMX Sigma and MMX2 Agile, are fairly easy to do this with, while others are quite difficult, like Vile, or impossible. I don't think it's possible to do this with the Face, Tank, or Giant Sigma Armor in MMX. Use Sub Tanks for this one, you'll need them. As an insanely tough extension to this challenge, try hitting Vile's armored mech as many times as possible with the Ryu fireball. I once hit him 50-70 times, so I can say for sure that there is, unfortunately, no secret ending that can be accessed by actually beating the mech. :P
Fight Dynamo Man with the Mega Buster / Forte Buster only, but let him use his recharge device 10 times. You can shoot the device to knock him out, but make sure he uses it.
I realize that some among you probably think I'm making a big deal out of some very simple stuff. Some of you have probably done all of the above stuff on your own. Well, here's a challenge for the true Mega Man elite. In any Mega Man X game, complete the entire game without obtaining any Dr. Light Capsules, Heart Tanks, or Sub Tanks. (In MMX1, wheree you have to collect the Dash Boots, don't play Chill Penguin's level until you've completed all of the others.) On top of this, use only the X Buster against mavericks and bosses (you can use specials against the mavericks the second time around, though). This is a pretty cool challenge in MMX1, and you'll often have to use a whole new strategy against some bosses, such as Spark Mandrill. MMX2 becomes something of an epic with this method, especially the wireframe Neo Sigma. I haven't tried this in MMX3, and I don't have MMX4.
Defeat every robot master in every NES game with the plasma cannon/Mega Buster, but don't slide, don't charge up shots, and make sure that you win with more than 14 energy points on your shield meter.
You think you're a Mega Man expert? Ha! Try some of these ego-boosting challebges. Each one is rated for difficulty. This page contains various challenges for Mega Man games. You'd be surprised how many different ways a Mega Man game can be replayed. Unless otherwise stated, each challenge implies that part of the challenge is not to use E-Tanks, Sub-Tanks, or Game Genie codes.