We recently purchased a gallon of Yamasa soy from our occasional sushi supplier, and the company claims to have been operating since 1645.
Any other contenders?
Do you consider the Roman Catholic Church a business?
The Hoshi Ryokan Hotel in Japan has been operating since 717 A.D.
Cool!
As for the RCC, that’s not exactly what I was looking for, but it’s food for thought.
Bass Ale had the first registered trademark in England.
The red triangle.
Industrial concerns: there’s a mining company in Sweden that’s been in business since something like the 1300s
Commercial retail: Everybody in the U.S. knows about the Hudson’s Bay Company sending traders to exchange European goods with the Indians for furs. Most of Canada and few U.S. citizens know it’s still in business, as a department store chain called The Bay
The answer for hospitality services (inns/taverns/restaurants) would probably depend more on the vagaries of preserved records than on the actual recordholder.
Bushmill’s Irish Whiskey has been distilled since 1608.
It’s owned by Diageo, though.
If you don’t limit the list to independently-owned businesses you’re essentially just asking what the oldest trade name is.
Fabbrica d’Armi Pietro Beretta has been in the firearms business since 1526.
The longest-running restaurant in the world is Ma Yu Ching’s Bucket Chicken House in Kaifeng, which first opened its doors in 1153. Previous thread on the subject.
Doh! That’s what I get for not searching. Here is a list from clairobscur back in 2002.
Link to site above.
I think that Beretta claims to be the oldest manufacturing company, but it looks like they might have some competition, seeing the French paper company mentioned that’s much older.
I’m still going to start saving for whatever shotgun they make in 2026 to celebrate the big 500.
I’m amazed that there are so many that are older than the Hudson’s Bay Company (founded 1670, IIRC).
There’s a pub in Dublin that claims to have opened in 1198. http://www.brazenhead.com/
I don’t think it’s owned by the original owner though.
And it seems I was equally amazed back in that old thread. 
That’s slightly misleading: the company survives but as a subsidiary of another. It’s not a family business anymore but you’ll still find carpenters wearing the Kongo Gumi mark at temple construction sites. It’s probably more accurate to say that the world’s oldest business changed hands after being controlled by the same family for 1429 years.
By the way, there’s an international association of long-lived family businesses. I can’t remember its name nor could I found it with a quick google search.
Yeah, my first thought when I read the OP was Kikkoman is older than that. Also apparently my first thought when this came up 5 and a half years ago (see post #5 in the linked thread.) 
Oddly enough, I vaguely remember posting in that thread. It’s weird having so many little pointless conversations archived and accessible like this.