5. Super Talking Time Bros - A fan made homage to Super Mario World. The engine and physics are nearly identical to the original, with a wide variety of over 100 stages to complete.
4. La-Mulana - A non-linear adventure/platformer that features 16-bit graphics and sound. The objective is to explore a tomb, collect various power ups, attempt to stay alive and reach the end any way you can. It's fairly challenging with quite a bit of trial and error, but once you get into the game it becomes a lot of fun.
3. Within a Deep Forest - An odd platformer that revolves around the player (in the shape of a ball) traversing around an open world looking for additional balls that can be selected that all have different properties. For example, the glass ball can accelerate quickly and has a high top speed but if it collides with terrain while moving quickly it will shatter, resetting you to where you were before attempting the obstacle. The soundtrack is very relaxing and provides good atmosphere, you should all check this one out.
2. Cave Story - Brilliant. Vibrant visuals, good sound effects, a great soundtrack, and an engaging story to boot. I don't want to spoil anything about this game so I will leave it brief, but EVERYONE SHOULD PLAY THIS AT LEAST ONCE GOGOGO.
1. Touhou (Series) - A series of SHMUP games that follow the exploits of witches roaming through a ghost world. Ok, so I really don't know the story or what's going on, but the games are ridiculous and a blast to play. Just about everything from each game was created by one guy, who goes by the handle ZUN, which is astounding to say the least. The games are fast based with little downtime, throwing waves of bullets and enemies at you with a plentiful amount of bosses and little intricacies that change from game to game to keep it fresh. The music is epic and stands alone, as in ZUN basically created his own music genre through the soundtracks of these games. There are also other games in the series that aren't shmups, for example Touhou 12.3 is a 2d fighting game that focuses heavily on projectile attacks.
You can find all of these games through a simple Google search, so go enjoy the free entertainment. And remember to support those whose products you actually enjoy!