We're operating on the same wavelength, DR Vixmom, since the speederbike sequence was the first one I thought of, too.
What I like about the Brosnan Bonds is how the pre-titles sequences have set up the rest of the story, along with being excelent action sequences on their own. (The inside joke, of Judy Dench, a.k.a. Jean/M, sparring with Geoffrey Palmer, a.k.a. Lionel/Admiral Roebuck, is a bonus in Tomorrow Never Dies.) I especially liked the double-action opener for The World is Not Enough, particularly the speedboat chase through London.
The What's Up, Doc? chase is a standout, too; amazing how closely comedy and suspense mix. The Indiana Jones films are all full of these set pieces. (Matt and I are thinking alike, too!)
One of my favorite chase sequences is from a not-too-well known film called Roadgames, starring Stacey Keech and Jamie Lee Curtis. Set in Australia, the big chase sequence works in reverse, as circumstances force the killer and the pursuer to move ever slower through the city, rather than faster.