I'll use WMP to check a file for corruption after being uploaded to an online repository. Other than that, playing back files on the same computer they were created in isn't going to reveal anything useful, since it's going to be affected by the same factors (speakers and room) as when you made the file.
Burn your music to a CD and listen to it in your car, and in anybody else's car who'll tolerate you. Put the files on a thumb drive and take them to friends' and relatives' computers. If you know anybody who still has a real "hi-fi" in their living room, definitely give your music a listen there. That includes crappy little bass-hyped sound systems like those awful Bose units intended for TVs. Each playback system, even bad ones, have something to tell you about your mix. Yes, even earbuds on an iPhone. Or the speakers built in to your television.
My own favorite alternate reference is a high-quality portable MP3/FLAC/WAV player, first through some good open-back headphones and then with some just-OK IEMs. Between them, they'll consistently let me know if I've made some dumb mistake.