Go to http://translate.google.com/. Type the name into the left-hand box, and say which language you want in the "From:" box.
Now, the left-hand box should show a little speaker icon in the bottom-right. Click that icon, and it will say the name as pronounced in that language. (Make sure your speakers are turned on first, of course.)
So for example, if you go to http://translate.google.com/#fr/en/Justin, the left-hand box's speaker button will pronounce my name more or less correctly.
As Gunnvor points out, it's not perfect, and I doubt they have every dialect we have to deal with, but it's usually reasonably good.
Better yet, you can do the same from an Android phone using the Google Translate app. I suspect that this is often going to prove useful when you get assigned a scroll to read and aren't sure how the vowels work...