Let me ask to everyone who doesn't like him, did you like Jay Leno? If so, this conversation is already a lost cause.
Jimmy isn't a comedian. He's a talk show host. What I like most about him is that he's the only one that seems genuinely appreciative of the guests he interviews. He doesn't act like he's on the same level of them, but always seems truly surprised that he gets to hang out with a bunch of celebrities for a living.
As Pyrate81 said, he has incredible connections to the music world. The Roots are an amazing band, and it's unbelievable that they choose to spend their time on a talk show. Jimmy's bromance with Justin Timberlake has resulted in some of the best stuff I've ever seen on any of these shows.
Like any new show, they need time to get their groove going. Moving to a new time slot means that they have have a different audience they need to tailor the show to. They also have new restrictions imposed by the network. One of my favorite parts of Late Night was the drinking games he had with the guests, but I doubt that will be allowed on The Tonight Show.
Give it time before you say you don't like it, but at least give it a chance first.
Side note, I'm also interested to see what Seth Myers does with Late Night, especially since he has Fred Armisen as his band leader.