Coffee (コーヒー kōhī) is quite popular in Japan, though it's not part of the typical Japanese breakfast. It's usually brewed to the same strength as European coffee; weaker, watered down coffee is called American. Canned coffee (hot and cold) is a bit of a curiosity, and widely available in vending machines like other beverages for about ¥120 per can. Most canned coffee is sweet, so look for brands with the English word "Black" or the kanji 無糖 ("no sugar") if you want it unsweetened. Decaffeinated coffee is very rare in Japan, even at Starbucks, but is available in some locations.
There are many coffee shops in Japan, including Starbucks. Major local chains include Doutor (known for its low prices) and Excelsior. A few restaurants, such as Mister Donut, Jonathan's and Skylark, offer unlimited refills on coffee for those who are particularly addicted to caffeine (or want to get some late-night work done).