Boots, booties, high-vamp loafers/shoes. In general - if the pant leg covers the top of the shoe while standing, then I think socks are ok, provided they're in the same colour family as the shoe/pant-leg.
I might be totally wrong about this, but this is the general idea. For instance, I might wear some booties with a pair of bootcut or flare jeans, and as long as the socks are the same colour as the boots/booties or the pants, then it's all good. I would only wear socks with flats if they are the high-vamp kind and with pants that are PPL - where the socks wouldn't really show, unless you just happened to cross your legs while sitting or something.
Does that make sense?
Curious to see what other YLF'ers have to say on the topic.