Key things with socks are:
quick drying - this means they wont get sweaty (so feel better), and also helps prevent blisters/bad skin
flat seams - friction causes blisters, so you don't want the ridges found in normal socks rubbing across your toes etc.
snug fit - just like the seams, any folds/flaps in a loose fitting sock is likely to lead to blisters.
If you're suffering with bilsters or don't like sweaty feet, buy some proper running socks.otherwise you can run in anything. Personally I spend a bit of cash on socks, as it seems daft to spend a fortune on shoes with the "perfect" fit and then wear cheap socks underneath (especially as socks last a lot longer than the shoes).