I think Anderson Cooper would be a great, trustworthy and professional replacement. Though I would LOVE to see Lewis Black. Your ideas?
some one with a not so dry sense of humor…
Bill Hader.
Bonnie Hunt.
If he were younger, maybe Kelsey Grammer. I honestly can’t think of anyone comparable who’d be in their mid-thirties, which would guarantee he (or she) would be around a while.
Definitely Weird Al Yankovic.
That answer is good for both questions, btw.
Wolf Blitzer. 
I’ve watched Jeopardy! quite a bit over the years, and while I like the game format, I never was a huge Trebek fan. It’s a great opportunity to hire someone who brings more to the show than a long tradition of being there.
Anderson Cooper won’t do it, though he’s an interesting choice. I wonder if Ken Jennings could do it. I bet Steve Harvey’s licking his chops over this (God help us).
Hell, drawing inspiration from my response at the top, I wonder if Andy Richter might take a crack at it. Yeah, I think he’d do well, and it’s a nice paying gig for not too many work days a year. Conan’s going to a half-hour format soon, isn’t he? Might behoove Andy to think about adding a second income in case this new direction doesn’t pan out.
Meredith Vieira
She was wonderful on Millionaire and would be even better on Jeopardy.
2nd option would be Anne Robinson from Weakest Link. She’d scare the jeopardy contestants just like Alex.
How about a rotating guest host slot? Since they record 5 shows in a day, it would be easy to have one host for one week.
I wouldn’t be surprised to see Ken Jennings. He has a great sense of humor and is already, more or less, part of the Jeopardy! family.
I also think he’d accept the job in a heartbeat.
mmm
Darrell Hammond
The answer to all such questions: Tony Shalhoub!
“This …, uh, person, …, um, is famed for …, uh, giving people …, er, uh, the Straight … Dope.”
Think of all the money the show will save with lower winnings.
NO love for Buzzy?
Bonnie Hunt is an excellent idea!
Tom Bergeron.
I’m not sure he has the right personality to host. He makes a better heel.
Will Farrell
Emo Phillips.
This was the first name that sprang to my mind.
I also vote for Meredith with Ken Jennings as runner up.
I dunno, Alex Trebek has sort of made it his own.
Meredith seems to have the right personality, and Ken already has a solid connection to the show, comparable, I think, to Alex’s.
Jeopardy has, I think, become known for, or adopted as some kind of standard for factual correctness. “If you saw it on Jeopardy, you know it’s true” sort of thing. With anyone else I think it would lose some of that and become just another trivia game show if you stick the wrong person in there as host.
FYI, here is a thread from last summer, in which we talked about potential replacements for Trebek. The motivation for the thread was a Fox News interview in which Alex Trebek speculated on a possible 2020 retirement and gave his suggestions as to a replacement. (Presumably this was before his cancer diagnosis.)