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Use high contrast between the background colour and text: WCAG 2.0 AA requires a contrast ratio of 4.5:1 for normal text and 3.1 for large text. Large text is considered 14 point and bold text, or 18 point or larger text.Grey text is all the rage these days, as are gray backgrounds. Dark grey text on a light grey background is difficult for many fully-sighted people to read, yet it persists on many websites (including HN — the visited link at the top of the page is #828282 and it's presented on a background of #F6F6F0. This yields a contrast ratio of 3.54:1, well shy of the recommended 4.5:1.)
The contrast problem also manifests on websites that have scrolling background images, which move underneath text and can create tricky contrast issues. Ironically, I've even seen these problems on accessibility-focused websites.
To be honest, I'm not sure how to fully solve this problem. I think as long as scrolling background images are popular, this will continue to be an issue. The only "fix" I can think of is to only use images that are mostly light or mostly dark, so that a single color of text can comfortably be read on top of them. But most images that people like to use in this scrolling are bright and dynamic, with light regions and dark regions. This doesn't bode well for text contrast or accessibility.