I have Arch Linux (downloaded from the Pi official download page) installed on my Pi. I would like to play videos with it from the command line without installing X. (Yeah, the goal is to make the Pi boots as fast as possible.) Is that possible?
It's possible and even encouraged. A nice command line player for the Pi is
omxplayer. It might be installed by default in Arch, otherwise it's available in the repositories. Omxplayer is written for the Pi, and uses the GPU for decoding video. It works extremely well and smoothly, provided that the video is in a supported format (h264 and mpeg4). Additionally, you can buy license keys for MPEG-2 and VC-1 in the raspberry store.
Btw, the more graphical media player XBMC uses omxplayer as a backend on the Pi.