Adventure & RPG Games
In these your character struggles through a storyline overcoming various hardships. In some you will see bosses and enemies, while others will see you picking up items along the way. Most of these have plots of good and evil, and many of them are platformers, where you see environments of fantasy and wonder. Many allow you to create your own characters and enact upon a series of tasks.
Fancy Pants Adventures 
These may be the best online games I have ever played, with a great storyline, inginuitive and inspiring gameplay, and a hand-drawn animated environment that suits the game perfectly. The Fancy Pants adventures are reminisent of Sonic the Hedgehog, with the same great momentum-involved stages and play, like sliding down frozen and slick hills, bashing baddies by jumping on them, and running vertically up walls at angles that are both wonderful and impossible. In World 2, things get even funner when you can wall jump up narrow chasms and dive down into the underground world, kicking around snails and trying to win a round of Fancy Pants Golf here and there. Vast new worlds await you in the epic chronicles of the Fancy Pants Adventures. The creativity that it took to make this is so insanely awesome that it deserves a 6 out of 5. -World 1- -World 2-
Armed with Wings 
This is an awesomely amazing game. You must try, as the last rebel soldier, reborn unto the world, to strike down a ruthless dictator and his minions with your sword. Your companion, an Eagle, is very helpful. Use him to distract enemies, activate switches, and pick up items out of reach. Each Stage introduces some new ability or harbors a boss. In the sequel, you play as the downcast emporor, fleeing from the palace that has now turned against him. You accomplices then tell you that the only way to regain the throne is to conquer all 5 commanders of the rebel army and fuse the elemental powers of their swords into a weapon that is suitable for revenge. With a uniquely crafted silhouette animation, it also introduces new abilities with each sword, as well as new characters and bosses, of course. The sequel also features select tracks from Super SmashBros. Brawl, and all the music fits well. These are exceptionally incredible, and I hope that the series comes back with more. 5 out of 5. -Play 1- -Play 2-
Pharoah's Tomb 
An older title where must explore the Tomb Indiana Jones style, carefully detouring monsters and traps. When you run out of health the game ends, and you must start from the entrance, so drink the healing vials to restore health. Pick up gold and treasures to further your score, and pick up Ahnkoras to open closed doors. Solve the mysteries of the ancient tomb, but be careful not to kill yourself along the way. As a forenote, I want to add that this is the first online game I ever played, so that's the main reason I dug up a hit this old. 3 out of 5. -Play-
