The Arabian Nights (Mahdi/Haddawy)
This translation purports to be closest to the “original” text, since it is a translation of the oldest surviving manuscript. Because of that, it contains only about nine major tales (all of them frames for other stories, of course). It’s a beautiful book, though (if you like that sort of thing), even in paperback, and the translation is excellent, and thoroughly modern.
There’s also a fascinating introduction, describing the history of the manuscripts, why this particular one is considered to be the most “authentic,” and obstacles encountered and decisions made in making this translation.
Husain Haddawy’s The Arabian Nights on Amazon.com