The Smiths. I'd consider myself a moderate Smiths fan. Certain tracks of theirs I adore, inspire me, can provide moments of glorious transcendence yada yada yada. However, upon listening to a Smiths album there are rather frequent moments where I will Mozza to stop being quite so self indulgent or where I simply think, "Christ, you've got a lovely voice but could you not tone down the warbling just a tad?"
Pink Floyd. Some massively enjoyable pop songs there. Also lots of hugely dull bobbins and worse fans.
Another well known group of boys spring to mind, but as I don't really have the energy to fend off accusations of trolling or the inclination to get into debate with their more rabid followers I think I'll leave that for another time.