You're so lucky!/ I envy you!/ I'm jealous of you!
As I learned it, 羨ましい as an exclamation does not carry much of a negative context, so perhaps a combination of these three interpretations would be best. However, in Western society, jealousy and envy are generally considered negative. Though this same impulse is also present in Buddhist tradition, I am interested in how this term takes on a (mostly?) positive nuance. Furthermore, are there any opinions as to why this exclamation is so common in Japanese, while an English (semi-)equivalent is not?
As a reference, here is a journal entry written by a Japanese native who is puzzling over how to express うらやましい in english:
日本語の「うらやましい」の中には「ねたみ」とか「嫉妬」の部 分があまりない（全然ないとは言えませんが）ような気がする のです。
だからこの場合、 ’They are lucky to travel to Korea." という軽いあこがれを 表現したかったのです。