Update: As some are pointing out, "non-European" can have two different meanings, one based in ethnicity and the other nationality. While Bergoglio is an Argentine citizen, his parents were born in Italy and he is ethnically Italian. Many citizens of Argentina, as in the U.S., are descendants of immigrants, and a majority are of European descent. So he not "non-European" in the way that a Filipino of Congolese pope might be, but rather in the way that an Irish-American cardinal is "non-European."
Previous non-European popes have included, for example, the very first one: Saint Peter, who was born in Bethsaida, which is thought to have been in modern-day Israel (possibly in the Golan Heights). It's a reminder that, although we think of the Catholic church as a European institution, the religion itself was founded in the heart of the Middle East. A number of other popes are from once-Roman-controlled regions of North Africa, a reminder that the Mediterranean was not always such a civilizational divide, although Christianity persisted in the region for centuries after the Roman empire's fall.
By my count, which is probably incomplete, he is the 11th non-European pope in the church's history, and the first in 1,272 years.
Here's a (again, probably incomplete) list of the non-European popes I was able to find in a cursory overview, with each pope's place of birth and the period of his reign:
1) Saint Peter: Bethsaida, modern-day Israel(33 – 64 A.D.)
2) Pope Saint Evaristus: Bethlehem, modern-day West Bank (97 – 105)
3) Pope Saint Anicetus: Emesa (today known as Homs), Syria (155 – 166)
4) Pope Saint Victor I: Leptis Magna, modern-day Libya (189 – 199)
5) Pope Saint Miltiades: Somewhere in North Africa (311 – 314)
6) Pope Theodore I: Jerusalem, modern-day Israel and West Bank (642 – 649)
7) Pope John V: Antioch, then Syria but today part of Turkey (685 – 686)
8) Pope Sisinnius: Syria (708)
9) Pope Constantine: Syria (708 – 715)
10) Pope Gregory III: Syria (731 – 741)
And now number 11! Pope Francis I: Buenos Aires, Argentina (2013 – ?)