If you can figure out a better chain, post it in the comments.
(Note: since we do all have the internet in front of us, just being able to make the connection isn’t really noteworthy. We’re talking style points here, people.)
Bruce Lee -> Kareem Abdul-Jabbar: “Game Of Death” (1978)
http://www.youtube.com/watch?v=8Rj7qiNFxd4
Kareem Abdul-Jabbar -> Julie Hagerty: “Airplane”
http://www.youtube.com/watch?v=_cANNP4ibgM
Julie Hagerty -> Albert Brooks: “Lost in America”
http://www.youtube.com/watch?v=upbjNQo4XxI
Albert Brooks -> Harvey Keitel: “Taxi Driver”
http://www.youtube.com/watch?v=1w7t48K0Wjg
Harvey Keitel -> Bruce Willis: “Pulp Fiction”
http://www.youtube.com/watch?v=vV4IBRic5_E
Unfortunately, I couldn’t find clips where the actors appear onscreen at the same time for the last three. (I don’t think they even exist for the last two.)