Like ashantiqua said, HDMI and DVI are pretty much the same thing. They carry the same video signal, with the main differences being that they have a different connector and HDMI carries an audio signal as well.
Some HDMI specs can carry other information, like Ethernet, but you wont need any of that for a monitor.
If you just want to connect your computer to a monitor and have no need for sound through the monitor, then it doesnt matter which you use. They will show the exact same picture with the same quality.
quote N00b Killer
If I wanted to use multiple monitors (say three or four), would it be wiser to go with a graphics card that has two DVI ports (and support for that many monitors) over one with multiple HDMI ports or one of each?
You will need a graphics card that has 3-4 video outputs to support 3-4 monitors. It doesnt matter what outputs they have as you can use which ever you want. For example, many AMD video cards have two DVI ports, a HDMI port and a Display Port. You can use all 4 connectors on 4 different monitors at the same time to show a different image on each one.