Media Player Classic for video.
It's simple, small, quick but full-featured, no BS or bloat, open source, updated occasionally. The interface is basic, it's just like WMP 6.4, so nothing fancy, but works fine. I can't stand WMP since v7. Maybe I just don't get it, but the interface in WMP 7/8/9ish is complete garbage and there seems to be no customization/options, and a ton of useless stuff like Now Playing, Media Guide, etc, well pretty much everything. I guess the library seems OK for music but no way would I ever use that when there is much better audio players. With ffdshow and MPC, you have a very tiny/simple combination that can play most any video format. If you need any Real or Quicktime support, get Real Player Alternative and Quicktime Alternative. I have them but haven't encoutered one of those POS formats in many months so I don't have either installed.
VLC Player is another one of the top ones like MPC but after trying it several times over a couple of years, I could never use it. From some screenshots, the interface looks good with some effort, but I haven't ever gotten it anything like I want so I can't stand it for more than a day. It takes a bit more customization than MPC (which requires almost none), but it's also cross-platform which MPC isn't.
Winamp for music. The library in the 5.x versions (unsure if they included it in earlier versions) is perfect for me, but other users may have different needs. Can't stand iTunes one bit myself. Though I used to be hardcore Winamp 2.9 or so, the newer ones are much better. The modern skins are great with ones like clearONE. And it still requires less resources than most players, and for what it does require is nothing for modern machines.