I love to browse over the WWW, and I see that lots of people on Yahoo Answers (lol) and other computer forums often have people asking what's a good video player. Being the anime, homebrew video, and software addict that I am, I went on a software rampage and downloaded (too) many things. Among these I have listed the players I found as the least unstable and most usful players. Feel free to discuss or add a recommendation here, and I hope it proves useful to you
CCCP - Community Combined Codec Project. Note, there is NO association with Russia here, except for the pun which the creators have so sarcastically put. It's the best codec and player pack I've ever used. The creators have originally aimed for it to be the playback solution for anime, but now lots of people use it for watching almost every common popular format. And don't worry, it has 0 bloat (unlike K-Lite
AHEM or Ace Mega Pack
MORE AHEM) and is continuously modified to improve playback, It supports .mkv with subtitles, which is awesome if you watch anime or anything with softsubbed subtitles, or videos with H264. Never had a problem, and they have a very fast support forum. For the people who are considering to get it... full installation is ~18MB, setup will ask you to disable conflicting filters, and includes Zoom Player and Windows Media Player Classic. My choice for all my computers

Sadly... it's Windows only.
MPlayer - CCCP's recommendation for Linux. And rightfully so. I've just got Ubuntu installed on my computer, and ditched all its audio and video players for this one. So far I haven't found anything it couldn't play. Supports all subtitles, and operates on its own set of codecs, so you don't need to worry about damaging filters or decoders. Best of all, you can pick a skin and your GUI is good to go. Even better, it's PORTABLE!

Works on Windows, Linux, and Mac. I love it on Ubuntu. Source code is available until GPLv2.
VLC Media Player - A very famous open source video player for Windows, Linux, and Mac. Tried it before, but I didn't like it very much. For one, it forcefully made all media files to play with it (I don't see any other player do that before) and the install was so messy I wish I had never used it. It's also portable and supports streaming protocols. The GUI could be better... but what I immediately did not like was how the player handled subtitles. If there are multiple external subtitles, all of them are showed at once, and you must manually set one. People have been complaining about it (like me) but they have yet to fix the issue. They also recently fixed a subtitle exploit. Use if you like something simple, although I would still recommend trying MPlayer first.
Media Player Classic Home Cinema - Based on Gabest's Media Player Classic. Has internal subtitle renderer and H264 decoding. Standalone, meaning it's portable. I tried it for a while, and it was actually really good. But I ditched it for CCCP =]
Media Player Classic - Standalone player by Gabest. Discontinued, spinoff is Home Cinema stated above. Included with CCCP, has internal subtitle splitter. Needs
Welcome to ffdshow though.
GOM Player: Free, simple, light media player. Patented technology to play broken or unfinished downloads of AVI files. Absolute bare minimum player. For playing unfinished downloads I'd still recommend VLC.
Edit: Why is the ffdshow URL not working, it keeps on going to Welcome to ffdshow and giving a weird http. Go
here. Sorry for inconvenience, no idea now it's going on.
I will add more later, and anyone who feels like adding their own recommendations is appreciated
On goes the rampage for my list of freeware recommendations RAWR!