First, the web continues to attract double-digit increases in advertising dollars. While this growth might slow, it seems unlikely to reverse. This means the web industry will continue to expand even if the economy as a whole does not.
Second, when the economy slows people tend to save and invest instead of spending. Given that many startups are driven by angel investment or venture funds, that's a good thing.
Third, web based and open source technologies are making huge gains in big business. They'll be increasingly attractive as companies tighten their belts. Given that the YC crowd is focused on this sort of development, that puts us in an enviable position.
I would start to worry if Google, Yahoo, Microsoft's web division, IAC, etc start making big layoffs. They could flood the market with competent programmers, driving down market rates and increasing competition for investment dollars. (Although I'm sure there are some companies fighting for talent that would love for that to happen.)
I think there's a greater risk of VCs moving to greener pastures - solar, biotech, etc - as web applications become commoditized.