Bebop scales were popularized by artists like Charlie Parker, Dizzy Gillespie, and Cannonball Adderley. The bebop scale is an eight note scale, with variants that include the dominant bebop and major bebop scales, the most common, as well as the bebop dorian, bebop melodic minor, and bebop harmonic minor scales. Form a dominant bebop scale by adding a major 7th note to a mixolydian mode. One of the advantages of the dominant bebop scale over a normal mixolydian mode is that when you play a dominant bebop scale in descending eighth notes starting from the tonic, all of the chord notes fall on the beats. Notes that are dissonant to the chord are used as "passing notes" between the chord notes.
Pentatonics are five-note scales (penta means "five" in ancient Greek) that are commonly used in jazz, blues, American folk music, and blues-based forms like rock music. A major pentatonic scale is just a major scale without the 4th and 7th notes. Form a minor pentatonic scale by removing the 2nd and 6th notes from an aeolian or dorian mode. Pentatonic scales are easy to use because they fit over a wide variety of chords, but the narrow range of notes can make them grow monotonous. The minor pentatonic scale is sometimes said to have an "oriental" feel.
Chromatic scales are made up of all twelve notes in a conventional western octave. Like a bebop scale, the "dissonant" notes of a chromatic scale can be used as passing notes so that the chord notes fall on emphasized beats. Chromatic scales offer a wide range of expression, but can sound very dissonant as they include notes that are opposed to the chord.
You can think of a diminished scale as a diminished chord with another diminished chord a whole tone higher superimposed on it. The scale consists of alternating intervals of whole tones and semitones, or half steps and whole steps. Diminished scales are very versatile, and while they sound complex, there are actually only three different scales. Diminished scales with the roots C, Eb, F# and A have the same notes, as do diminished scales based on Db, E, G, and Bb, and D, F, Ab, and B.