There are a wide variety of scales you can use in addition to the ones that derive naturally from the key signature. These other scales are either non-diatonic or abbreviations of longer scales. Some of these scales are derived from modes such as the following two pentatonic scales ("pent" is derived from the Greek word for five).

Major Pentatonic Scale

The major pentatonic scale is just the Major scale playing only five of the notes. (i.e. 1, 2, 3, 5, 6).

Minor Pentatonic Scale

The minor pentatonic scale is one of the most common scales of all but it is really just the Aeolian mode playing only five of the notes. (i.e. 1, b3, 4, 5, b7).

Blues Scale

The blues scale is exactly the same as the minor pentatonic scale but with the inclusion of a flat 5th in addition to the perfect 5th (1, b3, 4, b5, 5, b7, 1).

Melodic Minor Scale

The melodic minor scale is unlike most other scales as it is usually performed differently ascending (going up) and descending (going down). Ascending it is like the major scale with a minor 3rd (1, 2 b3, 4, 5, 6, 7 ) but descending it is the natural minor (1, 2, b3, 4, 5, b6, b7) (i.e. Aeolian).

Harmonic Minor

The harmonic minor is like the Aeolian mode but with a major 7th.

Whole Tone Scale

The whole tone scale is made entirely from whole tone intervals (1, 2, 3, #4, #5, b7). This scale is fairly rare but Stevie Wonder used it prominently in the introduction to his pop hit "You are the Sunshine of my Life".

Chromatic Scale

The chromatic scale has all twelve notes one semitone after another.