I just thought I would add my two cents.
Chuck Norris has actually improved his arsenal quite a bit since his early days.
Mr. Norris started in a martial art called Tang Soo Do. This is roughly comparable to Tae Kwan Do. As any Ultimate Fighting Championship fan knows, this style of fighting is not very effective. Since then, he has moved on to such brutal arts as muay Thai (Thai boxing - watch K1 for the power of this art) to Brazilian Jiujitsu. Brazilian Jiujitsu was made somewhat (in)famous by a somewhat small man named Royce Gracie from Rio De Janeiro, Brazil.
Jean Claude Van Damme has only studied Shotokan from what I understand. Shotokan is a very linear martial art with very straight punches. Traditional martial arts such as this are not very effective - especially against a Thai kickboxer or Brazilian Jiujitsu stylist. In a fight, Jean Claude would get his ass kicked by Chuck Norris - both standing up and on the ground.
Bruce Lee was very famous for his very good hand speed and for popularizing Okinawan weaponry. Unfortunately, Bruce Lee only studied stand up martial arts, such as: Wing Chun, muay Thai (the most complete stand up art, in his mind), Eskrima (Kali, Arnis, etc.), Savate (French "foot fighting"

, Judo (for throws), Pentjak Silat as well as American boxing. Unfortunately, his ground fighting techniques would be very sad. Judo has no counters for even a single or double leg shoot.
So, a couple notes - Bruce Lee was very infamous for getting in fights all the times on his sets (and a lot as a kid). Unfortunately, his fights did not go on very long and most of the people he went against weren't superb, trained fighters.
Chuck Norris was a point fighter - a good one though. Unfortunately, there is very little contact made in point fighting. This is not comparable to the hard core stand up fighting that great fighters such as Rob Kaman or Andy Hug or even Maurice Smith are famous for. This is the stuff where you can get penalized for hitting each other too hard.
My verdict? In his current fighting state, I think Chuck Norris would absolutely kill Bruce Lee - even in his prime shape. Why? Because as soon as Bruce Lee came in to punch Chuck, Mr. Norris would just shoot in, pass the guard, maybe get in a full mount and either go for something like an arm bar, key lock or maybe just punch him out. And, since Bruce is unfamiliar with ground fighting, he would probably give his back to Chuck.. which means rear naked choke.
But, if it was the 70s version of Bruce Lee versus the 70s version of Chuck Norris, I believe that Chuck would probably get beaten by Bruce Lee. Chuck's defense - especially his bad Tang Soo Do blocks and ineffective kicking techniques would probably open himself up for a very good beating.
Jean Claude would probably be happy just to be in the same conversation as these fighters.
But, really.. it's all about Kazushi "Gracie Killer" Sakuraba.
