...but you are nevertheless doing a heck of a lot better than "1/4 HD"!

You can achieve this with several desktop monitors, just gotta have the $$. :-)
We have a bunch of Sony 234b monitors (discontinued) that we picked up cheap from a dealer a year or so ago; 1900 x 1200, and with the Vegas secondary monitor, it's full rez, full screen, looks great.

You guys are a tough crowd, so let's break out the calculator.

1920x1080 = 2073600 pixels (HD resolution for 1080p)

This is what you can display on a 1024x768 monitor with 16:9 aspect ratio video window:
1024x 576 = 589,824 pixels
589824/2073600 = 0.284 HD

This is what you can display on a 1280x1024 monitor with 16:9 aspect ratio video window:
1280x 720 = 921,600 pixels
921600/2073600 = 0.452 HD

This is what you can display on a 1600x1200 monitor with 16:9 aspect ratio video window:
1600x 900 = 1,440,000pixels
1440000/2073600 = 0.707 HD

Thus, a 1024x768 monitor is doing slightly more than 1/4 HD .

Today, it's hard to find a graphics card at a reasonable price that will drive more than 1600x1200 with DVI output. I just bought a GeForce 7800 GS that maxes out at 1600x1200.