I'm also with the sing in your own accent crowd with an exception - for doing "theatre". When I sing "Wouldn't it be Loverly", as part of a two-person show we perform, I use a fake Cockney accent. Singing traditional songs it's always been my own accent that I use.

DonMeixner has touched on another point that I think about a lot. The singing of songs in a language that isn't understood by the audience. Apparent here at so called "Folk Festivals" which are becoming more and more "World Music Festivals". Granted that the overall sound might be wonderful. BUT! If a song has words, usually (Mouth music excepted), words are very important to a SONG. Even telling an audience what the song is about is not the same as hearing the poetry as it's sung.
Again there are probably a few exceptions. There have been times we've performed for audiences in restaurants and sung a few Italian songs at a table of Italians, a German song for Germans etc. Cheers, Joy