To be fair, you could score an entire film with just one of these instruments - but where's the fun in that?! (List suggested by @jonathan)
  1. Piano
    The cornerstone of basically everything written, ever. The amount stories you could tell with just a piano is never ending.
  2. Analog Poly-Synth
    Listen to almost every horror film to come out of the late 70's-onwards, and you'll most likely hear one. (People were actually using synths in films as far back as the 1930's once the Theremin was invented). The Sequential Circuits Prophet 5 was a favorite among people like John Carpenter.
  3. Cello
    I find the Cello to be one of the most versatile string instruments. You won't quite get the high, piercing shrieks of "Psycho", but it can still sing high enough to give you goosebumps.
  4. Bass Drum
    Hit it, brush it, shake it, kick it, punch it, sing into it, etc.
  5. Ukelin
    I found one of these at the Rose Bowl flea market, and immediately grabbed it. It sounded awful! The strings are rusted & horrendously out of tune, it was perfect. I used this extensively on my score for "The Diabolical".