Hillary Clinton - Liberal-Democrats (I can imagine her as having been an 80's SDPer)
Joe Biden - Labour
Brian Schweitzer - Labour
Andrew Cuomo - Labour or the Lib-Dems (probably a very big Blairite in the former)
Martin O'Malley - Labour
Howard Dean - Labour
Bernie Sanders - Labour
Joe Manchin - Labour
Jim Webb - Conservative
John Bolton - Conservative
Jeb Bush - Conservative
Chris Christie - Conservative
Ted Cruz - UKIP
Mike Huckabee - UKIP
Jon Huntsman - Conservative
Bobby Jindal - Conservative
Peter King - Sinn Fein of course
Rand Paul - Conservative (think Douglas Carswell
)
Mike Pence - Conservative
Rick Perry - UKIP
Marco Rubio - Conservative
Paul Ryan - Conservative
Rick Santorum - UKIP
Scott Walker - Conservative
Of course, one should remember that background, in addition to ideology, is also very important in determining which party one belongs to. For example, whilst Andrew Cuomo might hold what could be described as right-wing positions on economic matters, his father didn't, thus I think he would have ended up as a very Blairite member of the Labour party.