Serif typefaces tend to be thought of as classic and traditional, whereas sans-serif typefaces are thought of as more modern and contemporary. The fine details of serifs, especially the more delicate and high-contrast designs, don’t always display well on screens, especially at small sizes on low-resolution displays. I think all of this will change in the next few years though as high-resolution screens are becoming more common. Expect to see more delicate, high-contrast serifs being used on the web in the near future.
Font research done for you.