Dithering???
I'm considering having the website utilise dithering to allow it to look cool on a PC, but to take on a new life when viewed through a CRT monitor. Here are some examples of dithering that I like:
This is a classic example of dithering in a video game, from Sonic the Hedgehog 1. The waterfall is made up of only 4 colors, but it creates a transparent effect by dithering the colors together. The original image is on the left, and a composite of the dithered image is on the right.
Sonic Waterfall as it would appear on a modern screen, pixel perfect

Sonic Waterfall as it would appear on a CRT

Different kinds of dithering can be used for different effects. I'm personally fond of the 2x2 Bayer Dithering seen in the bottom left - it just feels like a nostalgic style for character portraits in games.