Nana Visitor wears a wig. Her hair is actually shorter than the short wig she wears on DS9. This may have changed after the first few episodes, since Nana seems to have lengthened her natural hair. It may have changed again (I'm going to have to bill her for making me update this section so often) since her hair is ridiculously short halfway through the third season.
Shatner has worn a hairpiece since before working on TOS. He switched to a "permed" hairpiece for the movies.
Frakes started wearing a hairpiece sometime after the first season of TNG when he started getting "scalp-burn" from the hot lights on the TNG set.
Spiner was *supposed* to be bald for one scene in "Unnatural Selection", but they thought Stewart might take exception to it.
Stewart was wearing a piece (with receding hairline) in the mind rape episode where Picard takes Bev to see Jack's corpse.
Kirk somehow avoided growing a beard when he was an Indian for a month in "Paradise Syndrome", but his sideburns grew longer.
McCoy had a beard at the beginning of ST1.
Data grew a beard for a short time in "Unnatural Selection". He also mentioned that his hair can grow.
Riker grew a beard after the first season of TNG and has kept it ever since. Frakes said at a con that he grew it in mock protest, but Roddenberry said he liked the "nautical" look it gave him.
Picard had a beard in Rip Van Riker's dream ("Future Imperfect").
Geordi was seen shaving in "Code of Honor".
Geordi started growing a beard in season six ("The Outcast"), but it's hard enough for him to emote in his acting when you can't see his eyes.
Worf has a beard because Klingons are proud of their beards. Dorn plans to grow a beard for season seven so he doesn't have to have one glued on each day.
Riker, Worf, and Geordi bet their beards against Bev Crusher's hair color in a sixth season episode.