This Late-late show is my favorite late night talk show, and it's still fresh and funny after 10 years on the air. (Has it really been ten years already?!). I still remember the very first show, and still remember some of the lines from Conan's first monologue.
I like the quirky, you-never-know-just-what-to-expect humor that Conan can spontaneously generate. I think he is able to do more "cutting edge" stuff - things that Letterman and Leno can only dream of. This is perhaps due to the fact that Conan comes on so late, that most viewers who don't have the necessary "cutting edge" sense of humor have already gone to bed - after having been suitably numbed by the more conservative routines of Letterman and Leno.
Though Letterman and Leno are both admirable comics, they have been relegated to little more than telling carefully thought-out jokes on their shows. Whereas Conan comes out acting spontaneously funny/crazy/weird; the show comes across as more of a mad-cap adventure for the viewer. So it's more fulfilling. Oh, and the Max Weinberg Seven: great band!
I'm glad that the Comedy Central channel plays the previous night's show every night at 7 PM then repeats it the next day at 1 PM. Now I no longer have to stay up late or even set my VCR.
(I think the only thing that helped me survive the Clinton presidency was the "talking lips" skit that Conan's show did all through the Clinton scandals. Those were priceless!)
***Edit*** I need to update my comment with more up-to-date info regarding the note about the Comedy Central channel airing repeats of the previous night's show. This is no longer the case. However, CNBC currently repeats the previous night's "Late Night with Conan O'Brien" at 4 P.M.