I don't listen to music while raiding, and especially not while PvPing. I need the audio cues to establish whether my spells are coming off, whether I'm critting (restoration shaman make a funny little noise when that happens), whether certain effects are landing, whether that warrior is Bladestorming, and so on. Of course there are visual clues as well, and for many people they will be sufficient, but I often find that, particularly in the Arena, I need all the help I can get! Also, while I do my best to keep track of every player at all times, in a 5v5 match, it's quite feasible that I can't keep my camera pointing at all 10 people, so the audio helps a great deal. I also find that music or TV can be distracting.
This is, of course, not leveled as a criticism to those who do play with music in the background, as ever with gaming is a case of diff'rent strokes for diff'rent folks. I can completely understand the use of music as a motivational tool or to amp yourself up for something challenging or to calm yourself down when things aren't going as you'd hoped.
But while I'm questing, or running dungeons, leveling professions, or running laps of Stormwind chatting to friends, I will often have some music playing or even the TV on in the background. I personally prefer some fairly easy listening, light music, to relax me while other players nerd rage. I'm currently leveling a discipline priest for the new Arena season, so there's sometimes a bit of anger coming my way when wipes happen, and music helps me stay calm! And, of course, there's the perennial Battleground rage to contend with, and music can help me maintain my Zen and laugh at it.
I listen mostly to fairly relaxed, mellow songs while I'm playing. Lana del Rey's Video Games is a current favorite, a very dear man recently introduced me to a lot of Van Morrison where I was only aware of a small part of his catalog, so that's on a lot. I also love listening to classical music while playing; Berlioz' Symphonie Fantastique is a particular favorite.
Do you listen to music while playing? Do you have the TV on in the background? And if so, what's your preference in listening material?