Red Burgundy wine is made from Pinot noir grapes, so a Pinor noir from another region probably will work well.
Wikipedia describes Pinot noir as “light to medium body with an aroma reminiscent of black cherry, raspberry or currant”, so any wine with those characteristics, such as a light Zinfandel or Shiraz/Syrah will be similarly substitutable.
cooking.stackexchange.com/users/285/nohat
In Mastering the Art of French Cooking , Julia Child says it should be made with a full-bodied young red wine.
She lists the following options: Beaujolais, Côtes du Rhône, Bordeaux Saint-Émilion, Burgundy, or a Chianti.
I've made it with a Bordeaux and can attest to it being delicious.
cooking.stackexchange.com/users/60/hobodave
It would change the flavor profile enormously, but making the equivalent of Boeuf Bourguignon with beer would probably be quite tasty.
cooking.stackexchange.com/users/1887/Martha F.
I've had great success in the past using a chianti.
cooking.stackexchange.com/users/2148/awithrow
I'd had success with Cabernet Sauvignon before (South Australia).
I tend to associate "full-bodied" (and hence better for cooking since delicacy isn't relevant) with Cab Sav and Shiraz varieties far more than, say, Pinot Noir.
Could be the characteristics of the local wines, though.
I'd be surprised if the choice of wine made a huge difference to the dish, however, as long as you didn't stray too far from the criterion of "ordinary red wine".
cooking.stackexchange.com/users/2545/Will Robertson
Try a Fuzion Malbec.
It's a cheap Argentinian that stands up really well.
In Ontario, it's about 8 bucks a bottle, and anything comparable is at least 12-15.
For god's sake, don't be cooking with a 30-50 pinot.
That's for drinking!
cooking.stackexchange.com/users/1148/Chris Cudmore
Try a Ribera del Duero ; you may be surprised.
cooking.stackexchange.com/users/2582/CesarGon
I certainly had a very delicious Boeuf Bourguignon in Calais one cold and wintry evening.
I complained that it was clearly not made with red wine and was rather pale and anaemic.
The chef came out smiling all over his face. "
Mais oui, monsieur, it ees my mother's own recipe.
White burgundy from my home town."
He showed me the bottle.
It said Grand Cru on the label.
So I proceeded to try to hide in my seat.
It was followed up by an excellent Roquefort from his cousin's place down in the Auvergne and he insisted I must have a good red wine (Burgundy) with this, on the house.
So we drank the whole bottle between the two of us!
Memorable evening!
cooking.stackexchange.com/users/33007/Jon
You need some liquid that is as tasty as wine.
Perhaps some beef consommé (Can o' Campbells!) would do the job.
I would add a bit of red wine vinegar, or balsamic, to make it a little bit acidic.
cooking.stackexchange.com/users/2181/Patrick
I've not tried it but my uncle was telling me
he's started using cider for this, googling turns up a few beef in cider recipes so he may not be losing his marbles just yet!
cooking.stackexchange.com/users/1797/Robin
Traditionally a Burgundy wine is used for  Beef Bourguignon . What are alternative replacements for this dish?
What are some alternative wines for Boeuf Bourguignon?
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<beef><wine><stews>
cooking.stackexchange.com/questions/5997
cooking.stackexchange.com/users/1302/crtjer
In  Mastering the Art of French Cooking , Julia Child says it should be made with a full-bodied young red wine. Possible options include Bordeaux, Chianti, Pinot Noir, Cabernet Sauvignon, Fuzion Malbec or Ribera del Duero. Other liquids that are as tasty as wine can be used, including cider and beer, although this could change the flavour profile significantly. You can use any full-bodied red wine. A Pinot Noir, Bordeaux, Malbec or Chianti are all good options.
You can use any full-bodied red wine. Alternatively, you can try beer or cider. Try a full-bodied red wine like a Bordeaux, Burgundy, Chianti or Malbec.