Rudin's Real and complex analysis, third edition (1987), page 9 of the French translation (1998):
Définissons d'abord un voisinage d'un point $x$ comme un ensemble contenant un ouvert contenant le point $x$. (Let us first define a neighborhood of a point $x$ as a set containing an open set containing the point $x$.)
It appears (thanks to @Martin for this) that the English and the French versions disagree since, on page 9 of the third English edition there is a parenthetical remark defining neighborhoods:
(A neighborhood of a point x is, by definition, an open set which contains x.)
This decision of the French translator of Rudin's book to modify this definition backfires on him, later on in the book, on page 35-36 Definition 2.3(d): there, the English text defines again a neighborhood as open and mentions parenthetically that some authors use the other definition; and all of this is translated faithfully in the French edition, in contradiction with the choice made earlier on to modify Rudin's text. Traduttore, traditore...
Munkres's Topology, second edition (2000), indeed stipulates that every neigborhood is open and, immediately after the definition, signals the alternative definition (pages 96-97).
All in all, it seems that readers of Rudin's and Munkres's books might not be completely taken aback by Wikipedia's version since both these authors, while following the other convention, explicitly mention this one.