Curve Fever - Simple, but fun. Kind of like a weird abstract driving snake game. Well-done, gameplay is smooth and lobby/ranking system is fair. The game is actually more fun if you don't play, gives you a sense of accomplishment.
Realm of the Mad God - MMO with permanent death, has bullet hell influences. Frustrating but fun to play with friends, definitely worth a try. Progress takes forever without money.
Stick Arena - Nice mindless action, haven't played in a long time though.
Territory War Online - Poor man's Worms. Quite fun, I haven't played TWO2 yet.
Legend of the Green Dragon - Text-based RPG. Very grind-heavy but minimalistic and can be played on most mobile devices. Beginners can really only log on twice a day for ~5 minutes, so it won't sap up much time to play. You can choose your own level of involvement.
Improbable Island - Mod of LotGD, much more complex and difficult to play but deeper and more strategic, also has a much larger player base. Storyline is pretty funny.
Kingdom of Loathing - Another text-based MMO with lots of humor. Very generous gameplay that encourages teamwork, but requires a lot of research on the Wiki to do anything.