Mac: Don't want to keep a pinned tab open playing your favourite tunes? Google Music for Mac is a standalone player that looks great, is feature-packed but lightweight, supports your media keys, and can play all of your playlists. Best of all, it's free.
Google Music for Mac works well. Technically, it's a custom wrapper that's accessing Google Music via the web, but it's a really good-looking one. It supports your Mac's media keys, so you can control playback without taking your hands off the keyboard. You can also switch among all of your playlists, stored music, and radio. If you prefer a more iTunes-y look, you can switch themes to match, and the app supports desktop notifications when the current song changes. If Google Music is your preferred music player, it's the best standalone player for Mac you can get.
Note: you should get this now while you can. The developer has made no attempt to hide the fact that he's using Google's own Google Music name, iconography, colours, layout -- just about everything that could easily get him shut down by Google on a moment's notice. He has no affiliation with Google at all, and the folks talking about it at Hacker News think that he's probably angling to get himself hired by Google (or his app picked up by them, at least). Hit the link below to grab it.