Yes they do, mine are fletched with a strong right helical.

A little something for the math wizards:

As Mobow mentioned your arrows don't make hundreds of revolutions on their way to the target generally like 2-5 actually. BUT, that being said they still spin at an extremely high rate... The proof's in the numbers.

For easy figuring we'll say the target is 20 yards away (60ft) and your arrow is traveling 300fps.

Arrow velocity: 300fps x 60s/min = 18,000fpmin
Distance: 60ft
Time of travel: 60ft / 18,000fpmin = .003min
Rotations: 3.5
Speed of Rotation: 3.5 rotations / .003 = 1166.7 rpm

So your arrow actually spins around 1100 rpm's.