There are plenty of anime series out there that are much more fun to watch while stoned, and one has to wonder, do the characters in those shows ever smoke weed themselves?
Realistically, the answer is probably no. Drug use is heavily stigmatized in Japan, and the legal consequences for recreational cannabis use can be pretty steep. Because of this, Japanese media doesn't usually depict drug use, and when drugs do impact an anime story line, it's often not a lot of fun.
That said, it's hard not to think of some characters as total potheads, particularly Stoner from Eureka Seven. Yes, that's his actual name. So, while there most likely aren't many characters who definitely, canonically do indulge in laughing grass, there are plenty of anime characters who probably smoke weed, or at least totally would if given the chance.
Mugen of Samurai Champloo has definitely gotten high at least once. He was part of a group that got ripped out of their minds after a field of what looked to be dank nug was set ablaze. While an accidental contact high does not a stoner make, Mugen's aggressively anti-authoritarian attitude fits nicely with the whole weed thing. He's definitely the type to light up just to stick it to someone who told him not to.
Why is everything such a drag for Naruto's Shikamaru Nara? There are a lot of reasons, but one of them is that he's probably smoking way too much weed. Seriously, this guy spends most of his free time spacing out and staring at clouds. You only do that if you're a nephologist, an artist, or a pothead.
The Yamanakas are some of his family's closest friends, and they specialize in growing and selling plants. There's probably a special Yamanaka strain that Ino, Choji, and Shikamaru spent most their adolescence inhaling. Sure, they risked getting murdered by Shikamaru's mom, but like true ninja in training, they always got away with it. As an adult, he and Temari occasionally eat pot brownies after Shikadai goes to bed.
Hatori Sohma of Fruits Basket is usually seen smoking something, and guess what, it's weed. Medical marijuana may not be legal in Japan, but Hatori clearly doesn't have much regard for the law. If he did, he would have called the police to report Akito for beating the sh*t out of all the kids in the Sohma family. Dude probably found a hookup in Sweden or some other 420-friendly country. He claims that it helps his eye pain so he can stay faded 24/7; yes, even while he's examining patients.
He's also not above using cannabutter in Akito's food to get him to chill out and stop attacking people. He once tried giving some to Shigure and Ayame in the hopes that they would stop flirting with each other for ten seconds, but the result was decidedly different, so now he keeps the kush under lock and key.
Stoner — Eureka Seven
Stoner of Eureka Seven is basically cannabis incarnate. His given name is actually Stoner, and he spends most of his time rambling about his extremely leftist political views. While Stoner is never explicitly shown rolling blunts, he does smoke cigarettes, which could technically contain just about anything.