BJ from Soul Eater. The man drinks it 24/7, carries a brewing pot in his travel case, and made a deal with the (benevolent) God of Death in exchange for coffee-related paraphenalia. Not to mention (he claims) his work suffered because his favorite coffee shop was no longer open.
Andrew Waltfeld from Mobile Suit Gundam SEED is legendary for his fondness for coffee, to the point that his XO once suggests ventilating his office.
L from Death Note is very often seen with coffee or tea, perhaps even more than the trademark desserts. He also seems to have a dubious relationship with sleep. Although his sugar obsession crosses over to his coffee and tea (6 cubes or more, every time without fail), he has been known to be so deep in thought that his cup has overflowed with sugar.
Detective Conan: Fanon always like to depict Conan Edogawa as one, who supposedly brews coffee so strong that only policemen and detectives can drink it... and he drinks it whenever he can. This is probably a Shout-Out to Sherlock Holmes' addictions.
Mamoru is a coffee drinker, to the point where he interrupts a romantic moment with Usagi to get a cup. In The Nineties North American English dub, his preference was changed to cocoa. .
Villainous Professor Tomoe shares this preference, which was likewise altered.
When not Dueling, Jack Atlas from Yu-Gi-Oh! 5Ds is seen at a coffee shop often, especially after the Dark Signers arc. He usually drinks Blue Eyes coffee, a shout out to Seto Kaiba's favorite card. And it's expensive as all hell. (3,000 yen per cup, or about $30 USD currently; note, however, this takes place a few decades into the future, so some inflation might have occurred by then.) Lampshaded and mocked to hell and back in "Tag Force 5".
Jack: Do you know my favorite coffee, Blue Eyes Mountain, do you know how much it costs? Correct Answer: Three Thousand DP!note The ATK of the Blue-Eyes White Dragon and the standard ATK of a Yu-Gi-Oh! Rival's ace.
Jack: Exactly! You know, that number somehow puts my mind at ease...
He tries making his own coffee in one episode; its okay, although Stephanie, the waitress at the shop, is very unhappy when he doesn't show up. (She, Carly, and Mina are constantly competing for Jack's attention in the second season. In the end, Jack really isn't interested in any of them, but they all part on good terms.
Chaud/Enzan from Mega Man NT Warrior/Rockman.EXE is seen drinking coffee quite frequently throughout the series. As in, it's the only thing we actually see him consume on screen until the 2nd season, Axess, and even then that piece of cake was pushed on him by Lan/Netto's mom. We don't see him consume anything other than coffee of his own accord until the 5th season, Beast.
Yoshimori Sumimura from Kekkaishi is a bit more G-rated — since he's a Triple Shifter, he needs a lot of coffee milk to get him through the day.