As most of the beer from the big companies are pale lager, for me there is not that much difference between a Asahi Super Dry or a Sapporo Black Label. When I buy beer, I usually go for the one I have not tried. However, I would say that in 2011, the Autumn Brew from Kirin was actually pretty good, and right now, the two Joel Robuchon from Ebisu are good too, a bid different from the usual products. However, I was disapointed by Asahi Dry Black, I was expecting if to stand out a bit more.
I also tried many craft beer, many of them are worth a try, but as they can be expensive, it's more of a special treat.
If it's only to enjoy the taste of beer and pay a low price, I would say Suntory Kin Mugi would be my choice, but I know people who are fan of Kirin Nodogoshi, that is also good for what it is.
There are certainly many seasonal beers and microbrewery options these days, so I would have to recommend a "nomihoudai" for alcohol fans. Surprisingly few tourists know that Japan has all-you-can-drink menus for a set price and set time (around 2000-3000 yen for 90 mins-120mins).
If I had to choose one beer, it would be Kirin Ichiban Lager brewed in Tohoku http://en.japantravel.com/miyagi/sendai-kirin-brewery-tour/8251 The taste is good, and it feels good to drink. That is because the company has helped communities through recovery projects in the area in the aftermath of the tsunami. Actually, the factory itself was hit by the tsunami but has since made a full recovery.