Happens at least once in Saber Marionette J. Otaru and Bloodberry have crashed a flying machine in the mountains; Bloodberry finds two fruit-bearing plants and hopes the juice from one will revive Otaru. Unfortunately, the pink one is more of a chili pepper than a fruit; Otaru not only breathes fire upon being revived, his lips swell up to the size of a bratwurst.
Mikoto from Mai-HiME gets this after she takes a bite of a spicy curry roll she ganked from one of the kendo students.
In Mai-Otome, Bruce Blan de Windbloom pretends to be drunk, then takes a drink and spits fire in Kid's face to distract him long enough for Lena to overpower the Schwarz agents in the train car in order to rescue Sifr.
School Rumble has a few instances of this, like Hanai (here◊) after drinking really hot tea. Yes, "hot" as in "spicy."
Although the fire is absent here, the second episode of Azumanga Daioh has Osaka getting a long, bad case of Hiccup Hijinks after eating a croquette filled with chili peppers.
One episode of Pokémon had some of Ash's Pokémon eating some spicy food; the one who ended up breathing fire was Squirtle...
This has happened a few other times as well: In one episode, Ash ate a Tamato berry (a spicy berry that looks like a tomato with spikes on it) and breathed fire. He was later shown with lips swollen from that. It's also happened to Team Rocket a few times.
In Kirby of the Stars, an entire episode had an Escalating War between Kawasaki's restaurant and Dedede's in making spicier and spicier foods. Everybody ended up doing this, except Kirby. Finally food spicy enough to affect him was found, just in time, as the flame spewing Kirby did allowed him to beat the Monster of the Week.
Yuri Cube's recipe for curry has this effect. Yuri loves it. Yuna couldn't stand it (but it was her only option for lunch that day).
In the dvd special Gundam Seed Character Theater this happens to Ray, after trying to sabotage Kira's dinner... But Kira unfortunately loves spicy foods.
The episode in Sailor Moon R, the one with the upgrade to the locket, has the Rei Eats Wasabi scene that was cut from the DiC dub. (It was actually a prank from Usagi, who put wasabi paste in a sandwich and then gave it to Rei...)
Similarly, in another R episode Minako gives the ill Rei a soup that's way too salty. Rei reacts in exactly the same way.
In one episode of Super Gals, Ran accidentally becomes a meek girly-girl. Her rival, Mami Honda, tries to crack Ran's unflappable smile by spiking a couple of fast food burgers with Tabasco sauce and hot mustard, which Ran eats without even breaking a sweat. Mami tries a burger herself and suffers from this effect, even after taking a drink. However, Ran does notice a burning in her mouth (though no fire) after turning back to normal.
In one episode of Shugo Chara!, Amu's charas give her a spicy drink to make her breathe fire and make Rima laugh. Rima's response is simply, "Super spicy gags are so out."
Happens occasionally in One Piece, the most prominent example would be when Mr 5 lets out a big ball of fire after being tricked into swallowing tabasco.
While the victims are more likely to breathe smoke then flames, this is pretty much the result of anyone who eats food made by Lum in Urusei Yatsura. As part of their Bizarre Alien Biology, Onis have a much higher tolerance for spice, and this desire to replicate her native tastes means Lum's Alien Lunches are too hot for humans to handle. Case in point, the first time she ever cooks in the anime, she gives Ataru a homemade lollipop... stuffed full of cayenne peppers.
The Naruto fillers have a particularly infamous arc named for the Curry of Life. Even though it is the titular character who truly invokes the trope, the only part that makes it truly worth watching is Neji's reaction to tasting it. Onbothoccasions.
Completely averted by Rock Lee, who has a fondness for the stuff... He and Neji at a contest would play out akin to Legolas and Gimli drinking.
Dora-nichov, one of The Doraemons spin-off characters has the ability to transform into a wolf when he looks at a moon-like object and can breathe fire when eating something spicy.
Yasuna's curry in Kashimashi: Girl Meets Girl reduced Yasuta to this and the rest of her guests aren't in much better condition. She likes it just fine though.