To answer this question, I first looked to Cave Story.
There's stories in them there caves.
Cave Story is a free platformer game by Daisuke "Pixel" Amaya, who programmed, wrote, drew, and composed the entire thing by himself over the course of five years, which is a pretty impressive feat considering that it takes me hours just to write a simple blog post. His original description of the game upon its release in 2004 is as follows:
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.
It turns out there's a little more to it than that.
After a short, unexplained cutscene, we're introduced to our similarly short and unexplained hero, pictured above in the cave where he begins the game. Leaving this cave reveals another, slightly larger cave, populated by strange critters and obstacles. By proceeding further into the cave, the hero can get a gun, which allows him to fight the monsters and clear away the obstacles. Then he can get through a door leading into another cave, from which more caves branch out, which allow access to other caves, and let's just say that there's a few very good reasons they call this game Cave Story.
One thing I've always liked about this opening sequence is its total lack of "tutorial" elements. There's nobody to walk our hero through his first jumps and deadly spikes, nobody to tell him what the deal is with this gun he found in the middle of a cave. The game doesn't even make the controls clear, although they're not hard to figure out. You're just thrown into this situation with no knowledge of what's led up to this, and as it turns out, your character is in the same boat. While it may be initially confusing, this helps to build a sense of immersion, that "you are your character", and this feeling is what drives the impact of the story that unfolds from this point.
You may have been wondering where the "story" part of Cave Story comes into play. As this blog runs, I will be talking about the varied and sometimes unexpectedly deep plots of games, and how their story elements make them worth playing. Cave Story's plot, for its part, is relatively straightforward. After making your way out of the first cave, you find a town populated by little bunny people who live in the caves for...some reason. You're introduced to a few key characters and the villains who make their lives miserable, and soon enough you're in the caves again, on your own against the machinations of the mysterious yet definitely evil Doctor.
None of these people are the Doctor.
It's a simple, "video-gamey" plot, which is mainly made to give some excuse to the various caves and creatures that inhabit it, and to give the player a bad guy to shoot at. Which is why the game's emotional moments often come as a shock. Characters can and will get hurt, even die, and the game has ways of making the player feel the impact of their loss, whether it's taking up a powerful weapon from a dying warrior or realizing, while just on the threshold of the final boss's lair, that a tragedy long since gone could have been averted. By the end of the game, the characters you met in the caves seem to reach almost human levels of motivation and compassion, and by this point you're playing to make them happy and give their sacrifices meaning as much as you're playing just to "reach the ending".
Ultimately, however, every element of Cave Story, from its surprisingly heartfelt narrative to the cute, pixelly graphics and retro soundtrack, serves to enhance gameplay. After all, when you play a game, you generally want to have fun, and Cave Story delivers fun in spades. While the story's out of focus, each level is really enjoyable to blast your way through. There's a variety of weapons, and while all of them have their uses, it's entirely possible to just pick your favorite and start shooting. Most enemies will fall quickly in the face of your withering sea of infinite ammunition, but that's not to say that the journey will be easy. Skillful jumping is often needed to get through perilous situations, and bosses are usually much tougher than the levels that precede them.
Fun fact: This frog killed me. Several times.
Outside certain boss sequences, though, there's really not a whole lot of thought you need to put into playing Cave Story. Just jump the gaps, fetch the items, fire your guns as fast as you can, and enjoy the story that's being told.
Cave Story was one of the first games that I really loved, and looking back on it it's not hard to see why. Even if it lacks a whole lot of depth, it makes up for that by just being fun, in both its caves and its story. If you're looking for a fun game, and you've finished your homework, I absolutely recommend downloading Cave Story.