Metal Gear Solid needs little introduction, it basically started a new genre of stealth games.
Metal Gear Solid has a very athmospheric background soundstrack, with the emphasis on background..you won't find anything that really stands out in the music (no guitar solos here).
The greatest track for me is 'Discovery', which you won't hear playing the game but it could've made for a great introduction track. The ping sounds in the beginning of the track line up perfectly with the opening cinematic of a submarine.
Another favorite is 'Furnace' which you hear while running around a blast furnace (surprise surprise). It has a drive and intensity to it that matches the molten steel around you nicely.
Finally, 'Cavern' is the first music you hear while playing (while you try your hand at sneaking past guards) and sets a dramatic tone for all things to come in the game.