It's really hard to pick a favourite, because saying a favourite is basically saying you prefer every single one of their songs to somebody else's, when that's just an impossible decision to make. But if I did have to pick it would be Dire Straits, a British rock band from the 70s/80s. They changed the way I looked at music entirely, have entertained me for countless hours and have got me through a tough time or two.
However a lot of other bands/artists come quite close, which is why I said it was such a difficult choice. Here are all that i can think of now. Notice the genres are a mish mash of classic/modern rock, blues and some psychedelia in there too. There are others I like too but these are the bands/artists which I like several songs from, not just one or two.
Eric Clapton, Def Leppard, Muse, Guns n Roses, Joe Bonamassa, Dream Theater, The Eagles, AC/DC, Mac Demarco