This is a freeware game that's kind of like Castlevania and Metroid combined.
It's really fun, and um...I'm gonna grab a quote to explain this.
Author's description of the game wrote:
Cave Story is a jumping-and-shooting action game.
Explore the caves until you reach the ending.
You can also save your game and continue from where you left off.
Studio Pixel Fan Page wrote:
This description is so humble that it borders on parody. Play now, laugh later.
You wake up in a cave. You shoot your way out of the cave, so you can get to a village in another cave. Then you have to go to a different cave, followed by...
Well, it's aptly named.
Cave Story is a freeware Metroidvania game by Daisuke Amaya, aka Studio Pixel. The plot is nothing to sneeze at, but it would be criminal to say too much about it: Half the fun is the way the game thrusts you into the action with no explanations, forcing you to figure out the plot by yourself as you go. Suffice it to say that there are robot soldiers, bunny people called Mimigas, and a Mad Scientist with a magic helmet and a Morally Ambiguous Doctorate trying to Take Over The World.
Of course, the gameplay is every bit as polished as the story, featuring a great difficulty curve that keeps it just challenging enough all the way through, a myriad of weapons with unique styles, and frequent, hectic, and exciting boss battles that are exhilarating and rewarding.
What's also notable is that, while the game is easily on par with any professionally-made Metroidvania game, it was created entirely by one man in his spare time. Daisuke Amaya wrote the scenario, drew the artwork and scenery, animated the sprites, designed all of the levels, composed all of the music, and programmed the entire game engine, all by himself over the course of five years. The game was a labor of love and it shows, in the best way possible.
Due to its popularity, there have been many ports. There's a Mac OS X port and a Linux port available. A port to the original Xbox also exists, as well as a PSP port, here (requires custom firmware).
Also, it's on the Wii and DSI Ware, as now you can pay for it. It's also coming to the 3DS as a full, not DLC game with complete 3D, new content, and more,
and it's scheduled to be released as a launch title[*].
And best of all, Daisuke has confirmed that a sequel is very, very likely.
* Not anymore. Meh.
So yeah. You should play this, it's pretty fun. I actually found out about this from Avlein in one of his videos.
The music is really awesome, too. It's 8-bit. The Wii version has remixed music, but it wasn't as good. There's also a ReMix version actually published by Nintendo itself, and is awesome-er.
The actual TV Tropes site with links and such to most of the various ports can be found