Although one can find a great variety of beer in Japan, the origins of the beverage stem from elsewhere. Japanese beers are often produced using technology and recipes sourced from European countries including Germany, the Czech Republic, Italy, and Belgium, among others.
In my country, the most well-known Japanese beer brand is Asahi Breweries, who started producing beer from 1889 in Osaka. These days, Asahi Breweries produce a large quantity of beer and soft drinks and are seen as a leader in the industry. Their number one beer is Asahi Super Dry, while their Asahi Clear is a lighter version. In Tokyo, close to the Skytree, you'll see Asahi Tower - the iconic gold building with a white top, resembling a beer with white foam. There are tours with beer degustations held there, which have been running for many years.
The brewery now known as Sapporo Holdings was found even earlier than Asahi – in 1876. After purchasing the large Canadian beer manufacturer Sleeman in 2006, Sapporo Holdings now own six breweries – five are located in Japan, and one is in Canada. Their main beer brands are Sapporo Draft and Yebisu.
Suntory has existed in Osaka since 1899 and is most well known for producing Japanese whiskey. Besides whiskey, Suntory produces beer, soft drinks, and even sandwiches. Like Asahi, Suntory organizes free tours which also come with a beer degustation, and more information about the tours can be found here. The tours are informative for both adults and children, though children and drivers can only consume soft drinks. The tours are held in Japanese, but since you can watch the process it ends up being quite self-explanatory. I was impressed when I visited the Suntory Brewery as it looked like a futuristic enterprise - it was so clean and sparkling! At the end of the degustation, feel free to visit the souvenir shop, where you can purchase sets of beer and beer glasses.
My favorite Japanese beer (after trying several different brands) is Kirin, and the Kirin Breweries in Yokohama and Sendai also give free tours. One remarkable feature is that every season you can try special beer with seasonal ingredients in cans with seasonal graphics. My advice is to taste different brands and choose the one you like best!