Played straight in Yu-Gi-Oh! 5Ds - Tetsu Ushio has thick eyebrows in a permanent arch to underline his status as the overdramatic comic relief.
In Season 0 as well to make Ushio appear more threatening.
Amarao from FLCL takes this to ridiculous extremes with his prosthetic Oddly Visible Eyebrows, which is visually made out of digitally-rendered nori seaweed sheets. The fact that they're fakes only serves to emphasize his immaturity. Believed that they also keep Haruko from channeling N.O. through his head like she does with Naota, but this is unconfirmed.
They actually are intended to serve the same function as a tinfoil cap, although it's probably less because he doesn't want it to happen and more because the things that do come through are embarrassingly small (the guitar Haruko pulls from his forehead is barely big enough to be a slingshot).
Amarao also gives a pair to Naota to wear as protection. Of course, they don't last long.
Amarao is at once an example of the trope and an inversion. His nori eyebrows are huge, but underneath them are ridiculously tiny eyebrows, if they even exist (which of course, serves as one of the series many, many Does This Remind You of Anything? moments.)
Dorothy's eyebrows are seen by many fans as one of her defining traits, to the point of becoming a Running Gag; one official Yonkoma actually has her using them to imitate various Gundams' forehead crests, and there is at least one doujin where they turned into hands.
Lu Anon from Mobile Suit Gundam AGE has noticeably thicker eyebrows than most of the other characters in the series.
Souten Kouro features more than its share of Big Ol' Eyebrows. Especially noteworthy are Cao Cao's; it's not that they're all that thick, it's just that he has four of them.
Klan Klein in Macross Frontier is female, and when she's her natural 30 feet tall her eyebrows are normal, but when micronized down to her peculiar Sleep Mode Size four-and-a-half feet, her eyebrows are relatively gigantic.
Jumbo on Yotsuba&! has these. Ena compares the shiisa figurine Asagi gives her to Jumbo largely because of the eyebrows.
Fuuka has a pretty impressive set on her too. Nonono, impressive eyebrows! Eyebrows!
England from Axis Powers Hetalia, as they make him look more like a gentleman (and part of the appeal is that they subvert the otherwise typically tsundere look he has). Sealand, Hong Kong, Australia, New Zealand, and the Australian micronations (Wy and Hutt River) have them too. In Hong Kong's case, this is supposedly because England placed a curse on them. Sealand has the same last name as England (and is, for all legitimate purposes, part of the UK) and is considered England's little brother. Curiously, Australia's eyebrows seemed even bigger than England's in his preliminary sketch, but he has regular eyebrows in volume 5. New Zealand shares the brows due to being another former British colony.
Characters that have thick eyebrows but are not linked to Britain: Cuba, Korea, Turkey, Ancient Rome, Denmark and sometimes Russia◊. India has noticeably thick eyebrows as well, but it's unknown whether it's an effect of him being a British colony or simply because he's Indian.
Mugi from K-On! is an exceptional case of a girl with noticeable eyebrows, which apparently run in the family (although her eyebrows are more potato-wedge shaped than they are bushy...).
When Azusa imagines a more determined Yui, she imagines her with thick black eyebrows fixed in an angry position. In the background of her fantasy, the other members of the band each sport a pair as well.◊
In the 'Final' episode they're pickled radishes. At least, in Yui's fever-dream.
Sumi from Amaenaideyo!! also qualifies as another exceptional case of bushy eyebrows.
Ken Akamatsu was a big fan of this trope; many of the girls in his work have this feature, notably the "ideal" lead in A.I. Love You. Author Appeal, right there.
Asakura Ryoko, a tertiary character from Suzumiya Haruhi actually has noticeably larger eyebrows than the rest of the cast. This has not gone unnoticed by some artists and the results, well, see for yourself.◊
Damos in Pokémon: Arceus and the Jewel of Life has these, but he's a very strong man with Yami Yugi's voice, so it's okay. However, his descendant Sheena has the same eyebrows on a very pale, narrow face with otherwise dainty features... it looks pretty strange.
Yuki Yoshioka from Mitsudomoe has an extremely noticeable pair. Nobody really draws attention to them, but they draw more than enough attention to themselves.
The Puchuus from Excel♥Saga develop these when hit as well as an over-the-top angry Gonk face.
Those faces - and their eyebrows - are Golgo 13's.
While none of the characters you'd expect to see in such an over the top anime have big eyebrows, Code Geass gives us Kyoshiro Todoh◊, of all people, who seems to be the spiritual success or to Treize and Dorothy of Wing when it comes to the forked variation. Given, they're both Sunrise series... Charles, meanwhile, does not have overly huge ones, but impressive, nonetheless.
Blue Exorcist has Kamiki Izumo, whose nickname in-series (and among the fandom) is "Eyebrows". Amaimon also has them.
Soujirou (the triplets' father), Yuki and her father from Mitsudomoe
Miyamoto Musashi from Yaiba, whose eyebrows aren't only extremely thick but also longer than his body (it helps that he's very small).
Miho Jufuku from A Certain Scientific Railgun has these. After her boyfriend dumped her, saying her eyebrows were ugly, she decided to knock other girls out and do Face Doodling to give them eyebrows like hers. She seems to have fallen for Saten after Saten said her eyebrows were unique and cute.
Mai Minase of .hack//Liminality is another female example, though it's rarely mentioned in the OVAs.