As ~E~ said, Metroid was the defining Metroid game (obviously). It had everything - action, adventure, puzzles, those heartpounding moments where you're left with 4 seconds to get from one side of the game to the other. It was brilliant.
Now, not long back, they made a remake. Metroid: Zero Mission. Basically it was Metroid, with Fusion graphics and a little suitless chunk at the end, in the space pirate base. It had more responsive controls and other awesome stuff. It was a better game... or was it?
Now, if you're a fan of retro games, ZM maybe wasn't to your taste. The Space Pirate mothership went against the grain of the 'all-in action' style of Metroid, with pretty much all of it in Stealth Mode. Stripped down so you have no armor, and only a pretty useless gun that only stuns Space Pirates, you have to make your way through the ship, from the bottom right to the top left. At this point, after a long trek, you finally get your suit back :D
Not a fan of avoiding things? Makes you paranoid, p'raps? Then the second half of this probably isn't your cup of tea. /However/ the first half will probably fit you perfectly. Even if you are a retro guy through and through, I would get this game (and when you finish the game, you unlock the original Metroid game, so it's a win-win situation... /if/ you want to play the whole game... it really isn't that hard).
Apart from that, if you /really/ don't want ZM, but want Metroid on it's own - buy it from the Virtual Console. If you have a Wii. WHICH YOU SHOULD!
Go on. You know you want to. It rocks. Seriously. Actually, I'm going to go play it now. Cya!