Tulip the giant in Jack to Mame no Ki after tearing off his clothes in a fit of rage. He actually spends the rest of the movie like that, despite having opportunity to get dressed.
Naruto: as of the Time Skip, Naruto now has green boxers with pink hearts on them.
One student is wearing these during the "underwear inspection" in the first episode of Sakigake!! Otokojuku. (Another has briefs with a bunny on them.)
Ranma is often seen wearing underwear with his name (or the first syllable thereof) printed all over it.
Also when Tsubasa is revealed to be a boy despite dressing and acting like a girl he is shown to wear pink boxers with yellow smiley faces on them.
Several characters in the Pokémon anime are shown wearing white/blue striped underwear, including Ash, a Hitmonlee's trainer in "The Punchy Pokemon", and Meowth imagines Giovanni wearing them while trying to cool down.
In a filler episode of Dragon Ball Z, a girl caught Gohan wearing teddy bear print boxers, and threatened to tell the school about "his secret" unless he went on a date with her (and she actually thought the boxers only added to his cuteness). However, Gohan thought she'd caught him removing his Great Saiyaman costume.
Classy Cat-Burglar Carson D. Carson spends most of Project Eden (The Dirty Pair movie) running around in his pink with green polka-dot boxers after the girls confiscate his clothes.
Subverted with Germany where he's shown wearing blue boxers with a patch sewn by Austria.
Katekyo Hitman Reborn!, The entire beginning of the series, especially when it comes to our favorite little Dying Will Bullet that burns off all your clothes (except your underwear, in most cases). As a matter of fact, Tsuna seemingly has a different one each and every time. The boxers return again when Spanner captures him... well... you know the rest...
Averted in Fullmetal Alchemist — Edward's boxers are plain and boring. However in a bonus-comic Arakawa is shown asking her assistants to try to design his underwear, and got some interesting suggestion such as Automail-boxers.
In the Cloverway English dub of Sailor Moon, a little boy drops his pants in front of Rini and says "I wear Sailor Moon underwear!" though he is shown holding plain looking briefs in one hand and his shorts in the other. In the original Japanese, he tells Chibiusa "Look at my little elephant!", doing his impression of Shin-chan.
Soul Eater's eponymous Soul apparently wears blue boxers with bones on them both in the manga and the anime (and since the series was animated by BONES...yeah).
In Episode 2 of the Little Lulu anime, when Tubby strips down to his underwear as one of his tactics to try and scare Lulu, he is shown to be wearing a pair of navy blue boxers with sky blue splotch patterns on them.
The eponymous Space Dandy is revealed to wear black boxer briefs with lightning bolts on them; as first shown in the episode "The War of the Vests and Undies."
In a similar, offscreen example, Tsukasa in Lucky Star is particularly embarrassed by absent-mindedly wearing character print underwear on Measuring Day.
Also similarly, Yuno in Hidamari Sketch was also hugely embarrassed when her kitten-print undies were revealed in a locker-room prank. (Why does it have to be yonkoma...?)
A Running Gag on Blue Seed involves Momiji displaying a different animal on the seat of her underwear when she does her Once an EpisodePanty Shot. The other characters maintain a betting pool on just what's going to show up on her panties any given day.
Asuna of Mahou Sensei Negima! was embarrassed to no end when a magical sneeze from Negi destroyed her clothes, showing her teddy bear panties to the man she had a crush on.
On the cover of Bleach volume 3, you can see that Orihime's wearing polka-dot underwear.
In Hayate the Combat Butler, Hinagiku is normally serious... until she was revealed to wear (rather cute) frilled orange panties that didn't suit her at all (although she says she likes them)
In one of the episodes of the second season of Sayonara, Zetsubou-Sensei, Ikkyu is so distracted by Chiri's Bell Pepper panties that he manages to forget that they were attacked by an alien race piloting Humongous Mecha.
The first episode of Himesama Goyoujin has Aoi Misuzu slip on a discarded soda can, showing off her tanuki-print panties to the rest of the tennis club.
The movie Ultimate Teacher has Ganbachi humiliate Hinako by removing her skirt in front of the whole class... revealing her lucky kitty gym shorts. Naturally, men from all over rush in to have a look. Hinako's maturity is later reflected when she defeats a gang by showing that she's now wearing plain, white panties.
In a Running Gag for the Tantei Gakuen Q anime, Kyu (but not the viewer) ends up seeing up Megumi's skirt for a variety of reasons (though never because he intentionally flips her skirt up; sometimes the wind blows strongly while she's wearing a short skirt, at others she trips on her feet...) and blurts out what pattern is on them on a semi-regular basis. The patterns include things like teardrops and bunnies.