Sort of the precursor to DVD and still very popular in Asian countries. VCD has VHS like quality and SVCD has SVHS like quality.
The .bin file is the binary data and the .cue file is metadata.
I use Nero and you can just select the Disk Image option and point it at the .cue file. You'll wind up with a VCD (or SVCD).
Look for the .DAT file in the MPEGAV directory on the CD. It's a standard MPEG2 file. WinAmp or Windows Media Player should play it.
Alternatively, if you don't want to burn it to a CD you can get a free program called
DaemonTools which will allow you to mount the .cue/.bin as a virtual CD. After installing DaemonTools you'll have an icon in your system tray that you can right click on and mount the virtual CD. It'll show up in Windows just like a regular CD or DVD.
Finally, I wholeheartedly recommend another free program called
VideoLAN for all your video playing needs. It's able to play just about everything out there (and if you want, stream the video over a network).