The Order of the Knights of St. John, (also known as “The Knights of St. John”, “The Knights Hospitallers”, “The Knights of Rhodes”, “The Knights of Malta”, “The Sovereign Military Order of Malta”) were founded in 1099 as a religious and military order in Jerusalem, which also operated a hospital. They defended the Holy Land during the Crusader era, and then defended Cyprus, Rhodes, and Malta (successively) against the Ottomans.

They still exist as an institution today, headquartered in Rome. They are widely recognized as a Sovereign power, and mainly run hospitals around the world.

The University of Karueein was founded in 859 in Fez, Morocco, and is the oldest university still in existence in the world.

The University of Bologna in Italy, founded in 1088 is the oldest university in Europe.

Kongo Gumi Co. Ltd., a construction company in Japan, was founded in 578, and has been in business ever since, building the Shitennoji Temple and Osaka Castle, among many other buildings.

I can think of a few alcoholic brands and companies that have been going for centuries.

In Italy, the oldest winery is Barone Ricasoli's, which dates back to the 12th century. Then, the Frescobaldi family used to be a big name in banking in the middle ages, they started a winery in 1308 called Frescobaldi too, which is still running today. Then, of course, there's the legendary Antinori, one of Italy's finest wines, which dates back to 1385 and is still making outstanding wine today.

In Belgium, a lot of breweries are very old. Affligem is the oldest, I think, founded in 1074 (it's also a Benedictine monastery, some of Belgium's finest beers are made in monasteries). Grimbergen brewery, also a monastery beer, dates back to 1128. But it's not just some obscure brands that are very old: Stella Artois brewery dates back to 1366. They are based in Leuven, not far from the university which is equally old (founded in 1425), proving that beer and students are inseparable throughout the ages.

In France, Chateau de Goulaine dates back to the year 1000, which is the oldest winery in France. The oldest cognac is Frapin, which dates back to 1270. The oldest champagne is Gosset, which dates back to the 16th century.

In Germany, I know the Furstenberg brewery dates back to 1283. That's the only one I know, but many other breweries would certainly date back to the middle ages.

edit: fixed Leuven's founding year...

The Keiunkan in Japan is the oldest hotel in continuous operation, having been founded in 705 AD

Obviously this won't hold a candle to any of the institutions in Europe and Asia that have been operating much, much, longer, but the Hudson's Bay Company has been around since 1670. It started as a fur-trading company but now owns and operates several retail brands, including Lord & Taylor and Saks Fifth Avenue.

Also their blankets are cool.

What about Freemasonry? There is a lodge in Scotland that claims to date back to 1140, but I don't know if this is generally accepted by historians.