But I think the greatest motorcycle chase scene was in Top Gun when Tom Cruise chased an F18-D on his Ninja 900 while pumping his fist in the air like a total goob.
u'r so glib! ...that was cool til about 1990...
Glib I am, but even at the tender age of 17, I felt sorry for him in that scene.

On the serious vein, I think one of the greatest chase scenes, and
the greatest motorcycle chase was the opening scene in Mad Max. Who could be cooler than the Goose? After taking his bike into a slider that stops against a trailer (caravan), the driver asks Goose, "What happened?"
The Goose, pulling off his shades, says, "Don't ask me, man. I just got here myself."
I think it alone was worth the price of admission. My second bike favorite, to agree with red_haint, was McQueen in the Great Escape. I remember watching it as a kid and thinking that his jumps were the coolest thing ever. That gives him a shot at best car and motorcyle chase scenes ever.
[edit 6 Feb: Added McQueen]