I've got my setup going where I can switch between computer and Xbox 360. I wanted to use my monitor so I could see the HD graphics. So far, awful awful awful. They look really terrible. They look worse than games on my computer in 800x600 resolution. I'm easily getting MUCH better graphics from my VGA hookup and on my OLD big screen TV with component cables... this seems backwards. 
 
I realize that with HD, you can see flaws probably more accurately, but this isn't just a small downgrade... it's nearing PS2 era graphics.

make and model of monitor? 
 
i have my xbox 360 connected to my dell 3008wfp via hdmi and it looks incredible.

Did you go into the settings on the 360 and change it to 720p?

Sounds like your 360 settings are off.  How are you connecting to your monitor?

The monitor is directly connected to the XBOX with an HDMI cable. I've tried it in 720p and 1080p both in the Xbox settings. The monitor is a Hanns-G... couldn't see the model number. I'll have to investigate that... 
 
Just got through trying Red Dead, Darksiders, and Monday Night Combat. All looking pretty bad. 

You need HD cables too
 
EDIT: Oh you do, I have no idea then.

You're doing something wrong.  Monitors are usually 16:10.  Are you sure your monitor is 1280x720 (16:9)?

Bad cord?

" You're doing something wrong.  Monitors are usually 16:10.  Are you sure your monitor is 1280x720 (16:9)? "

This is my monitor... 
 
http://www.hannsg.com/US/EN/Products/LCD%20Monitors/Common.aspx?productId=140

360 looks loads better on a CRT monitor but you might have to play around.  The 360 uses its video scaler in modes that aren't 720 or 1080 so use those if you can.  My CRT doesn't go up to 1080 and isn't widescreen but I've set it to 720p widescreen then used the screen adjust to squeeze it vertically so it's got black borders, and I'd really advice CRT users to do the same if they haven't got a widescreen monitor and they can do that, or the same if you've got an LCD that supports 1 to 1 mapping.  Actually make sure your monitor isn't set up to scale the image if that's in the settings, that's another reason it would look like crap.

What are your 360 Display settings?

Screen is 720p. Color Space is  Source. Reference Levels are Expanded. Display discovery is enabled. 

I used to hook my 360 up to my monitor and it was absolutely awful -- can you describe your exact problem with the graphics? For me there were jaggies everywhere constantly, it was like I was playing 640x480 without any AA. To be honest, console graphics are underwhelming nowadays anyway -- expecting anything near what a PC can do is folly.

Make sure you set the 360 to output video in the native resolution of the monitor. Sending a non-native signal tends to look bad, even worse if the aspect ratio is wrong as well.
 
If you can't use the native res at least choose one with the same aspect ratio.