Crude humor can mean a lot of different things, but the general consensus is that it's the type of humor that's described as "below the belt". These are the types of jokes and situations that only adults would understand. Live-action examples would include the National Lampoon movie franchise and several movies about the college "frat culture" that was popular in the 1980s.
Some of the best anime uses this crude humor to get laughs even in shows that aren't considered comedies. Often it's one character that has a reputation for making rude jokes, while on the other hand, it might be the basis of the whole show.
7 Black Lagoon
A series about a band of mercenaries isn't exactly going to be fluffy. They call themselves Black Lagoon and they work in Roanapur, a lawless corner of Thailand. When otherwise mild-mannered businessman Rokurou Okajima gets mixed up with these ruffians and decides that he can't beat them, so he joins them.
The show is primarily a drama, and it's produced by Madhouse so it looks great, and the adult themes of the show overlap with the jokes. Black Lagoon speaks most of its crude humor through the character of Revy, an uncompromising nihilist who uses inappropriate references and slurs with violent abandon.
6 Cowboy Bebop
Although it's a drama primarily, Cowboy Bebop is about a gang of bounty hunters, gamblers, and misfits, so there are going to be a few crude jokes here and there. The main character himself tends to favor dark or cynical humor while other characters, like Faye Valentine, are more outspoken about their motives and their quips.
Director Shinichirō Watanabe helped design the characters, and they were developed with certain archetypes in mind. Faye Valentine, in particular, was modeled after the legend of the American West known as Poker Alice and she's got the rugged frontier mouth to prove it.
5 Gin Tama
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Reading a description of Gin Tama makes it sound like a serious drama about a hero with a small team of allies fighting monsters in a post-apocalyptic world. However, this is one of anime history's most popular comedies, and a lot of its laughs come from crude humor.
The mix of genres is one of the things that confused critics about this series at first, with some complaining about tonal problems. Some of the jokes were also specific to Japanese culture and hard to localize, but luckily great strides have been made in recent years in translating crude humor, and the show is as popular as ever.
4 Samurai Champloo
Most of the uncouth humor in Samurai Champloo comes from its rudest character, the scruffy and uncivilized Mugan. This series does star three bitter teenagers, however, so there's plenty of crude humor for his companions to enjoy, too. Even Jin, who seems so demure and reserved, turns out to be a ladies' man and isn't always polite about it. Even the young and innocent Fuu has quite a colorful vocabulary.
Shinichirō Watanabe also directed this series, and the characters are designed and organized in a similar way that reflects certain parts of his own personality. The plot follows the template of a "road trip" and very few movies that use that framework don't also use ample amounts of crude humor and odd coincidence.
3 Dragonball
It's easy to forget that the original Dragonball series was a comedy, since the tone shifted to more of a serious drama in later years, with stakes on a galactic scale. Not only was the first season intended to be funny, but it used a lot of crude humor to get laughs, and every character was implicated in one way or another.
The Hunt for the Dragon Balls saga, which is the first part of the season, actually ends with a crude joke. Oolong, the shape-shifting pig, thwarts the enemy by wishing for a comfortable pair of underwear. He gets them and proceeds to wear them on his head for the rest of the show.
2 Tentai Senshi Sunred
A parody of the popular superhero genre, Tentai Senshi Sunred asks what our caped crusaders are up to when they're off the clock and sometimes it's pretty crude. The main character, Sunred, is trying to retire from the superhero life but the arch-villains that were a part of his career won't leave him alone.
Despite his reputation for being a hero, Sunred isn't a very nice or likable person. He's lazy and gross and generally acts like a complete jerk to everyone. Most of the laughs in this show come from Sunred's personality and habits and his half-assed efforts at a normal life.
1 Panty & Stocking With Garterbelt
This series doesn't even try to be coy but goes below the belt right from the title. Panty and Stocking are the Anarchy Sisters, and they've been exiled from heaven for a variety of shocking and sometimes cringe-worthy transgressions. The only way back is to redeem themselves by defeating the malevolent ghosts of Daten City.
Taken seriously, this could be a horror or occult anime, but all the inappropriate jokes make it a comedy. There are plenty of other hilarious examples of crude humor too, like random nudity and exploding toilets, so even viewers who are accustomed to crude humor will be impressed by Panty & Stocking with Garterbelt.