Hard task, 'cause I'm a working musician and have played in cover bands for years now, so there's plenty of such songs and bands for me...
In general I wouldn't say I like Coldplay or care for them at all, but I'd say they earned a bit of respect from me by the brilliant debut album, Parachutes, and there is a song there that I really love, called Spies.
Some people mentioned Duran Duran and I have to add my opinion too: I think they are a good band, a bunch of great songs and more then adequate musicianship... My problem with them is that when I was a kid all the yuppies liked them and they stood for flagboys of the fashion and style that was something I found disgusting at the time and also don't like to be reminded of nowadays. I was 9-10 at the time and through my older brother I had developed a taste for music that was, in my opinion, a bit advanced for my age, all the kids I went to school with, and, actually, those a few years older, like my cousins, used to listen to Duran Duran and similar popular stuff, like Nik Kershaw, Paul Young, Madonna, while I was into the Doors, the Beatles, Bob Dylan and, a bit later on, Nina Simone. So, as I felt those kids that listened to Duran Duran and all the contemporary stuff were all fakes and yuppies, which most of them actually were, I also associated the band with such prejudice from my side. Later on, as a grown up and a professional musician, I discovered a lot of their stuff actually isn't that bad at all, as the matter of fact songs like Save a Prayer or Ordinary World are great, but I wouldn't go that far to say I actually spend my time listening to the band, I just know and respect them,.
I could say a similar thing about A-Ha: I like Hunting High and Low, but I hate the whole period in the music history when all of that occurred, especially the mainstream MTV 80's. I know there must be some good songs there, but I like to stick to some vintage stuff or some interesting things that were going on in music unnoticed by the mainstream media, who, at the time, were into Boy George and Limahl...