DVI-I / DVI-D Compatibility?
 

Can I use a DVI-D cable on a DVI-I Input? (i.e. the DVI-D cable would be missing a few pins on the DVI-I plug)

Yes, No, depends?

(Basically I am looking to hookup my computer with DVI-I output to my LCD TV (with HDMI input) using a DVI-D to HDMI cable.)

What's the difference between DVI-D and DVI-I anyway?

and while I am on the topic, what's the difference between dual-link (more pins) vs single-link (less pins)

read http://en.wikipedia.org/wiki/Digital_Visual_Interface

has all the info, cause it depends :)