For me it's Cream. I'm not sure why. I recognise their songwriting talent but at the same time I find them a bit... cheesy, especially I Feel Free.
Another contestant would have to be the Beach Boys. I like a tiny fraction of their stuff (namely All Summer Long (the song) and bits of Pet Sounds) but a lot of their tunes just won't stomach with me, although I can see the influence they've had on a lot of awesome bands since.