What's the origin of the stock phrase "tall, dark, and handsome"?

Suits and Tuxedos may be the source of the "dark, and handsome" part. Wearing nice clothing can also make people "stand taller," because they are proud of their clothing.

The earliest use of it in print that I can find is from The New Monthly Magazine and Literary Journal, 1833. It is from a "paper" titled "The Story of Hester Malpas," by L.E.L.:

Hester now looked at her aunt, who was the very reverse of what she had imagined : she had always thought she would be like her father, and fancied a tall, dark, and handsome face.

According to an excellent post found at Wordwizard.com, and as seen in the citation above, the phrase was originally used to describe women as well as men up until the early 20th century (see EL&U discussion here). Also of note, the popularity of the phrase spiked after a movie by the same name was made in 1941 starring Caesar Romero.

Probably Europe.

Other cultures outside of Europe (with darker skin) seem to think that lighter skin is more beautiful.

This is a phrase associated with the upper class Europeans along with another allied phrase, namely, "prince charming". Trace it back to Europe especially around the time that the "swarthy" Moors were the masters of Spain. The Shakespearean play Othello is a definite clue. The search will also no doubt find that during the same period the European upper class prided themselves in being extremely pale and free of the tell-tale signs of having had to spend any appreciable time in the Sun. Hence the term "blue blood" that came about as the extremely Sun deprived skin would exposed the veins in a bluish hue thereby giving the illusion of one having blue blood.

I can antedate Callithumpian's 1833, at least by dropping the and. The earliest is in 1815's Scenes on the shores of the Atlantic, Volume 2 By M. F. Dickson:

This Ngram suggests the shorter version is more common:

Before these years, the adjectives tall, dark can be easily found together in many places, such as describing men, mountains and trees.

I've just heard an anecdotal report on "Travel with Rick Steeves" radio show (American Public Radio) that the Scots believed that to have a stranger who was tall, dark and handsome appear on New Year's as the "first footer" meant good luck all year - as Viking conquerors would have have been blonde, and there to collect taxes or worse. No real etymology research here, but makes a fun thought, and would likely predate much of the written practice.

Not to directly answer the question about the phrase, but I'll point out that biologically, men and women are believed to be hard wired to seek certain physical traits in partners that ensure that they will hook up with a good mate. For women, a tall male is more likely to be big and strong and able to defend her and provide for her. Within any stable ethnic group, men are more likely to be slightly darker in skin color, as they do not have to produce as much Vitamin D (via sunlight on the skin) as women do (for bone growth in fetuses and nursing babies). And "handsome" can mean a number of physical attributes, from facial symmetry (indicating good genes) to sharp features (indicating high testosterone levels and thus likely fertile, as well as an aggressive defender). All three together suggest that a man would make a good mate, and the female should be receptive to his advances.

Men, of course, have physical attributes they look for in females, indicating potential good mates, and call this "beauty". Note that all this assumes heterosexual orientation -- I can't tell you what gays or lesbians seek in a partner.

Now, before anyone blows a gasket, downvotes, or edits this, I understand that you might well consider this to be more along the lines of pop psychology than proven science, and that's your right. It's quite plausible, but certainly not proven. And of course, a society, its cultural norms, fashion, personal tastes, and even who is making advances towards whom, can override whatever hard wired attributes are considered desirable in a potential mate's physical appearance. I'm just saying that "tall, dark, and handsome" may well reflect a deep, even hard wired, female viewpoint on what appearances make for a desirable male, and the language reflects that, rather than being an artificial literary construct.