Shadows is a good game, and important story-wise, but it's not great.
The story: You follow Dash Rendar, a bounty hunter akin to Han Solo, in his interactions with the Rebellion that ultimately lead to a confrontation with Prince Xizor, a rival leader to Darth Vader vying for the Emperor's favor. That's the basic plot, and that's all you'll need to know for the purposes of this review. The story is told through cut scenes wherein a picture of the character is shown at the bottom of the screen, accompanied by text (there is no voice acting). It's very similar to PC games of the time, and very 1990's, but that doesn't mean it's bad. In fact, the cut scenes do a very good job of moving the story along.
The sound: The soundtrack is classic Star Wars, plus some newly-composed John Williams' pieces, so of course the music is perfect, and it fits the tone well. The effects are fine; blaster fire sounds like blaster fire, probe droids make their iconic noises, etc. No real problems there.
Now for the meat and bones of the game: the actual game play itself. Shadows plays like a run and gun shooter, with options for first-person as well as third-person. The controls are simple to learn, though the execution is clumsy at times (though not as bad as some people have said). For example, the game can be overly sensitive, or sometimes very less sensitive to your actions, particularly with regards to movement. You may press the joystick a little bit, and Dash will do nothing; when you push it harder, he falls off a cliff (which is actually kind of funny). The point is, it feels kind of like a chore at times to control Dash, but for the most part it controls relatively fine. The first mission, unlike most of them, has you piloting a snowspeeder during the Battle of Hoth, and it plays very similarly to the Rogue Squadron series of Star Wars games. In fact, I'd say it sets the standard for those games, because it is very, very fun. Unfortunately, the rest of the levels never really match the greatness of the first, and so the game doesn't ever realize its full potential. Another issue I had with the game play was certain times where the game really didn't provide any clues whatsoever on what to do or where to go next, so you can find yourself lost and confused relatively easy (the Gall canyon level comes to mind).
One other thing I should mention is a plot hole I discovered; there were wampa beasts (those snow creatures from The Empire Strikes Back) on Gall, which is a desert-like moon of rocky plains, so that doesn't make sense, but whatever. Yes, I am that nerdy. I also should mention that one of the boss battles with IG-88 the bounty hunter is one of the most difficult (and creepy) boss battles I've played, and it's extremely likely that you'll die quite a bit before beating him the first time, so the difficulty isn't the most balanced in the world.
Graphically, this game looks as you'd expect it to look, being one of the first Nintendo 64 games made available. The amount of detail isn't very high, save maybe for Dash and a few other enemies, etc. But everything looks rather good for its time. That's pretty much all I can say on that.
Overall, Shadows of the Empire is fun while it lasts, but it isn't really a game I can say I want to come back to repeatedly. The story is enjoyable, and it sets a precedent for future Star Wars games, so I recommend it to Star Wars fans and casual gamers alike, though for the latter I'd say just play it for fun.