I love guys in little white socks, but the best length to wear really depends on the guy and the shoe. Some guys look totally sexy wearing sneakers without socks. Others guys look stupid like that. (Unfortunately, I'm one of the guys who looks stupid.) If you look good without socks, you can opt for no-show, but they aren't always truly no-show. Depending on the shoe and the size of your foot, "no-show" socks sometimes show, in which case ankle socks look better.
I also really like the look of crew socks bunched down. As simcha says, it shows off the guy's calves, but I don't see that look very much anymore. It seems like everyone goes for the low-cut socks instead.
No-show or low-cut socks should only be worn with shorts, however. If you're wearing socks with pants, then guys shouldn't wear socks that expose any skin. It just doesn't look right.