Tom Snyder (1995-99)
IMDb

I think before this ever came out, David Letterman appeared on The Larry Sanders Show, and someone asked him who he was gonna get to do a post-Late Show show, and he joked "Tom Snyder," whom I had never heard of. At least, I thought he was joking, but then he actually got Tom to do this show for real. Anyway, it was um... I dunno what to say. I sometimes liked it, but that's probably because I was so tired at that time of night. Or maybe it was just kinda kitschy or something. Tom was just this sort of old guy who rambled alot. It was funny. I think he got some good guests on there, though. It was certainly always amusing to watch him chatting with hip young celebrities and whatnot....

Craig Kilborn (1999-2004)
IMDb

Starting in 1999, Tom was replaced by Craig Kilborn, who had previously hosted The Daily Show. I don't think I ever watched very much of The Late Late Show, during Kilborn's tenure. I mean, less than I did when it was hosted by Tom Snyder, probably. But it was okay.

Craig Ferguson (2005-2014)
IMDb; Wikipedia

The show's third host was Craig Ferguson. Before this, I basically just knew him from The Drew Carey Show. But really, he's the best host the show has had so far. Really very funny, in a sort of offbeat way, perhaps in part because he's Scottish. I dunno. I still don't really see the show except for a few minutes when channel surfing, on rare occasions. But it's really quite good, so I kind of hate myself for not seeing more of his tenure than I did. Especially near the end, I really meant to try to catch the show, but... I just can't stay up that late.

James Corden (2015-present)
IMDb; Wikipedia

So... Ferguson left the show in December 2014. Then there were a few months with guest hosts, and I'm sure I read a magazine article about how good they were, but of course I never got around to checking out that transition period. Then in late March of 2015, James Corden became the new regular host. And I really hope someday I get around to watching.