Ahh, a classic trio. The phrase grew out of the hardboiled pulp detective
stories and crime dramas of the 1920s and 30s. Writers like Raymond Chandler
and Dashiell Hammett
began using all sorts of hep slang
in their books, and a lot of it has stuck with us today ("don't get any ideas", "wise guy
", and others), and tall, dark, and handsome is no exception.
Generally, the phrase means trouble in the form of a stranger. Although the description sounds like a dream guy, it's almost always implied that the girl who falls for this guy is letting her weakness for men get the best of her, a decision she'll come to regret. Note that the dark does not necessarily mean dark-skinned, or even dark-haired, but rather mysterious, determined, and generally with a "dark countenance" to back up their sincerity.
There was a 1941 movie starring Cesar Romero called Tall, Dark, And Handsome (and boy, was Cesar the ideal tall, dark, and handsome fellow) about a hood having to deal with his mistress, his underlings, and his rivals. It's pretty good but forgettable, but does go to show how fast and far that term had spread.
Some other actors noted for being tall, dark, and handsome include: Clark Gable, Montgomery Clift, Rock Hudson, Dean Martin, Warren Beatty, Charlton Heston, Clint Eastwood,
Al Pacino (not tall), Jack Nicholson, Burt Reynolds, Daniel-Day Lewis, Denzel Washington, and Russell Crowe, along with no doubt countless others. (Are there any women you'd call tall, dark, and handsome? - Inflatable_Monk suggests Greta Garbo. I guess you could throw Marlene Dietrich on the fire, too.)
Update: Finally! Rushton came up with a woman to fit the bill: Lucy Lawless aka Xena, Warrior Princess. Kudos to you!