An old rule of thumb is simply that sans-serif fonts are easier to read on screen while serif fonts are easier in print.
I agree, and will go further. It's more than just a rule, it's a fact. This has less to do with style than it does with the practical and utilitarian concern of making content easy to read.
Serifs are little lines that come off the ending of letters. The effect is to create an easy reading experience as one letter leads to another, led forward by the serif. This works well in print where the resolution of a newspaper is more or less 200 DPI. A computer monitor renders text at a lowly 72 to 100-ish DPI, which is not enough to prevent eye strain when reading Serif fonts.
However with the increasing use of smartphones with high resolution displays around 300 dpi, the use of serif fonts may become a better choice. Perhaps best to split the difference and sniff for the best font?
Verdana is the workhorse font for online legibility. It is wide spaced between letters and easy to read for long periods of time. Arial is another sans-serif font that works well online but the spacing between letters is tighter, which can introduce reader fatigue. The advantage is that you can cram more words into a limited space and still be legible. A font like Verdana is useful for when you want to encourage a longer time on page.
Perhaps a Serif font online is like those uncomfortable fast food seats that encourage people to finish up fast. In the case of a website, who knows, they might encourage people to click on the ads...
[edited by: martinibuster at 3:11 am (utc) on May 25, 2013]