I saw Melissa Rapp play "Circles" in SF using Piano+Vocals... it sounded great! She's a local singer songwriter:
www.melissarapp.com

Also, Elton John has rocked out with piano/vocals for a long time. Check out his stuff too.

Hmmm, let me think here... have you heard the Jerry Garcia & Howard Wales albums? I don't know if you're into the Grateful Dead at all, but they sound pretty different when they play together anyway. I highly recommend Hooteroll, that's a great album IMHO, and the keyboardist (Wales) plays a prominent role. Merl Saunders and Melvin Seals were others who played with Jerry, and I believe they have a lot of their own stuff as well.

I actually like Pink Floyd a lot for piano based rock- people don't give Richard Wright the credit he deserves for shaping a lot of their sound. Of course there's Dark Side, but then he is also quite audible on most of Meddle, Atom Heart Mother, Animals, Wish You Were Here, and Saucerful of Secrets. I also like much of the piano work on The Wall, even though it's mostly not him (Nobody Home is one of my favorite tracks on there). Wright also has his own album called "Wet Dream" that I have not yet obtained a copy of but sounds good from the samples.

My favorite rock pianist has to be Page McConnell of Phish, have you heard their early stuff? Junta, Lawnboy, and Rift are rich with gorgeous piano melody, all HIGHLY recommended.

I'm not a huge String Cheese incident fan, but Kyle Hollinsworth is also a very competent player who plays a central role in their sound. He has a solo album out now too.

Medeski Martin and Wood and also Robert Walters 20th Congress are both piano based, funky/jazzy stuff that I like a bunch.

Tea Leaf Green plays pretty striaght-forward rock and is mainly piano-focused.

Joni Mitchell plays simply but quite beautifully, I have always thought.

For stuff out of the hippie arena (if you're not into that sort of thing) there's of course people like Ray Charles, Herbie Hancock, and Billy Joel (all of which I'm sure you've heard before). Funny though, I can't think of many rock pianists outside of the type of music that I listen to that have enjoyed much success.

I'm interested in making music like you described too. Keane is a good example of a piano-based band (trio). Not terribly complex but damn catchy. Only other one I can think of has already been named, Ben Folds.

i can't believe no one listed the Dresden Dolls yet. yum.
Also, its not lead, but its amazing in Muse, or at least in the album Absolution.
I heard a really good rockin' Chick Korea album once, but didn't get the name, and now all i can find is overly jazzy stuff. I know there's more, but i can't think of to much now...

oh, and like most the other's in the tribe, my band rae is piano rock! i perfer the term olde wave though.