I've had several inquiries about the correct pronunciation of Boeuf Bourguignon. I'll try my best to tell you, phonetically (and without a French accent), how to say it. (While you're here, won't you please take a moment to check out my Etsy store? Thank you!)
Boeuf is pronounced boof. It rhymes with poof.
Next, bourguignon. Start with bow (like bow and arrow), then guin (like Guinness beer, or New Guinea. It's a hard G follwed by "in"), then yawn. Put it all together: bow-guin-yawn.
I hope this helps, but, if you're still not comfortable with your pronunciation, just call it by it's English name: Burgundy Beef.
Edit: I never would have imagined this would be the most frequently viewed entry on my blog. Every so often I get an extremely rude comment quibbling about the pronunciation of boeuf. There's not an exact English translation I know of to identically duplicate the French pronunciation of boeuf. Listen to the two pronunciations in this link and you'll see how minor a difference there is. Boof is about as close as you're going to get in English (American).
Edit again 7/1/14: Despite the above disclaimer about the rude comments, they continue. They always seem to agree that there's not an exact American English equivalent of "boeuf" as they proceed to try. It's so much easier to just click the links in the above edit and remove all doubt. Sheesh!