If all of the chords are major chords, than I'll rename that A# as a Bb... I've played a song similar to this (it went G, G, F, F, C, Bb, C, Bb, G) and through some trial and error rather than sitting down and thinking about it, I found that the G Minor Pentatonic or G Blues scales sound great over the progression.
Think about it, the G Blues scale contains G, Bb, C, Db, D, and F. Analyzing these notes in relation to chords will show why it sounds so good.
Notes relative to the chords:
C Chord = C, E, G
G Chord = G, B, D
Bb Chord = Bb, D, F
F Chord = F, A, C
The G Blues scale adds the b7 and b9 to the C chord. It adds the b3, b5, and b7 to the G chord. It adds the b3 and b6 to the Bb chord. Finally, it adds the #5 to the F chord. Playing a minor scale over a major chord implies a blues/rock sound (one plays an E Minor pentatonic scale over an E7 chord quite frequently in blues progressions).
"You must stab him in the heart with the Bone Saber of Zumacalis... well, you could stab him in the head or the lungs, too... and the saber, it probably doesn't have to be bone, just anything sharp lying around the house... you could poke him with a pillow and kill him."
- Aqua Teen Hunger Force, The Universal Re-Monster