I'm afraid this thread's going to be rather Windows-centric, as I don't use iOS or Linux. Personally, I use Media Player Classic – Home Cinema. I've found it's the best media player because it's very lightweight and plays almost any format. I used to use VLC media player, though. What about you? edit — I forgot about music. I use foobar2000 for music playback and Winamp for editing ID3 tags (it's got the best interface for it, I think). I use iTunes if I'm changing out what's on my iPod, though.
I use WMP for my music library, just 'cause it does certain things that iTunes doesn't. All music and video files are defaulted to MPC ... but I also have VLC for anything that MPC can't handle.
Used to use iTunes for music, but have just been using my phone because of the better speakers. I use Clementine for FLAC files, and Spotify for music I don't own.
I'm surprised to see that so many people use Windows Media Player (unless "WMP" stands for something else, heh). I switched from WMP to VLCmp back in the day because of how many problems I'd had with WMP playing nonstandard file types. Also, and I'm sure this is going to have an obvious answer, but are certain media players better equipped to play flac files than others? I'm genuinely curious. I've always just used whatever media player I was using at the time to play flac files because I've never had a good pair of headphones or a good set of speakers, so the sound quality didn't really matter all that much to me. (Of course, I'm not really an audiophile; as long as something sounds good, I'm fine with a standard 192kbps/44.1khz rip.)
I use GOM Player for videos and Winamp for music (though I like this Music app in Windows 8.1 – might as well start using that here and there).
iTunes for general MP3 music playing VLC for general anything playing Chrome using Spotify's Web Player for the music I don't have and don't want to download