Title should be pretty explanatory.
Two bands come to mind, Dream Theater and Red Hot Chili Peppers.
For DT, this song kind of does it all: http://www.youtube.com/watch?v=ad_chktqWLo
Such a sick melody to open the whole song. The around 2:30 the vocals come on and the whole song becomes unlistenable. I've also seen the band cover songs like Master Puppets. You can see John Petrucci guitar circles around Kirk Hammett, but again the singer is insufferable.
Next RHCP. I know Anthony Kiedis has his charms to people, but he just sounds like a bad karaoke guy.