Devil May Cry 3. I remember smiling thinking "Holy shit, this is awesome" during the final boss fight, even though I was getting my ass handed to me.
Mega Man Zero 3. Yet another game that gives you a character with all kinds of sweet moves and weapons, yet still kicks your ass. Being able to dash-jump off a wall at an enemy and cleave it in two with a lightsabre is all kinds of awesome. Shield Boomerang is awesome too. Z-Sabre + Shield Boomerang = Jedi Captain America
Contra 3. The weapons are well-balanced, the controls are flawless (the "stand still and aim" button comes very much in handy), the two-gun system means you're not completely screwed over when you die (because you get to keep the gun you didn't have equipped when you die), the weapons are well balanced (even the default machine gun has its uses) and the game is freaking HARD. But not in a cheap way. Any game that can give you a gun that shoots RAPID-FIRE HOMING MISSILES with infinite ammo and STILL kick your ass is doing something right.
In conclusion, cool moves/weapons + challenging but fair difficulty + the number 3 at the end of the title = Awesome.