Starfox 64 was, is, and will continue to be a great game.
Graphics: This was probably the peak of graphical goodness 12 years ago. Even today, I see some games that can't match the graphical quality of starfox. Plus, it only runs slowly when there is complete chaos (too many explosions and around 50 enemies) on the screen.
Gameplay: Not too complicated, but a bit more sophisticated than button-mashing. There are three types of attacks, and a bunch of bonuses that you can get for the regular laser attack. There's also a bunch of sophisticated maneuvers that you can do, like sideways flying or barrel rolls. Plus, the difficulty is perfect. It starts out easy, but not too easy, and then works its way up the difficulty scale. The last level is hecka hard.
Music: A delightful score! It varies from epic to creepy at the right moments, and has great melodies. And the "mission complete" music really gives a sense of satisfaction, somehow.
Story: A good story, but not as compelling as other parts of the game are. You can understand everything and sympathize with fox and all that, but I just don't think it's that awesome. However, a lot of characters have great lines. Falco in particular when he's arguing with fox.
Multiplayer: meh. not so good. You basically fly around in circles firing ur lazah.
Other notes: Lots of secrets, and different ways to play the game! The story mode is short, but there are so many different paths you can take by finding secrets or changing paths on the mission select screen. Also, you can affect certain things that happen later in the game if you do them early. For example, if you beat star wolf in the third level (playing without secrets here), he won't come back in the second to last level.
Overall, a stupendous game, and I love it. I'd totally recommend that you pay the $10 for it. For such a great game, $10 is quite a deal.