DVD Players
Audio
Either Digital Coaxial or Digtal Optical (toslink) to connect from the player to the receiver (Do you remember the model number so we can look it up?)
Video
You can run straight to the TV or through the receiver
If through the receiver, then Component from DVD to Receiver
If not through the receiver, then Component (or HDMI if DVD and TV have it) from player to TV
Computer
Audio
Depending on what you're playing on the computer, you have a few options
Stereo analog with one 3.5mm to 2xRCA cable
Multichannel analog with three 3.5mm to 2xRCA cables attached to the multichannel input on the receiver
Digital connection from computer to receiver with Digital Coaxial or Digital Optical (toslink)
Video (are you doing this?)
Especially if you have an HDTV, you'll want an HDMI or Component connection between the computer and the TV/receiver
If your TV doesn't have HDMI or your vid card doesn't have DVI out, hopefully it has a component hookup
If not, then S-video is acceptable (and generally fine for an SDTV). Your receiver doesn't do conversion to Component, so if you're running any non-component sources, you'll need to hook up the monitor our hookups of each type to your TV from the receiver. Maybe even hook up straight to the TV with video in that case since you'd end up having to switch the inputs anyway and you'll end up buying less cables that way...
TV
If you're using the TV's tuner, then you'll want to run audio out to the receiver as well.
Not knowing what model your TV is, this could be stereo analog output or a digital output.
Game Systems
This is going to depend on each system for what's available.
I believe Component might be the best connection type for Wii and the original xbox?
Wii audio will be stereo analog RCA connection?
Original XBOX digital optical is an optional audio connection?
Without knowing more about what specific products you have or what way you want to connect things, we can't do more than guess.