I prefer serif types on screen if the display technology is good enough. On paper, I can think of nothing other than serif. Apparently the belief that serif makes reading easier is true. Reading something printed in serif feels like munching and gulping, making real progress. Also, serif has an elegance. What's special about this elegance is that it never disqualifies serif for running text. Usually types that have great emotional impact are good for titles, but not for running text. That's not the case with most common serif fonts. They're good for both.
But for me, none of the above applies to Times New Roman, the most popular serif font of our times. Its pointed letters look like military fence, which nobody wants to rub their eyes againt. Sure, Times New Roman has rounded edges in some places, but some less-rounded siblings look more smooth to me.
What I actually prefer is serif types that have less contrast between thick and thin strokes. This includes and excludes members from both old-style and transitional serif families, despite what the classification says. Bitstream Charter, Palatino and Liberation Serif look great. Deja Vu Serif is bigger, but that's good on screen. And there's Gentium, a magical blend of elegance, sweetness and kindness, which I'd prefer to read a fairy tale in.