Just as Yaoi Fangirls exist out there (Yaoi Fanboys exist too, but you have to look really hard), there are Yuri Fans. For those of you not familiar with Anime terminology, "yuri" means "girls love" (and "yaoi", "boys love") in Japanese, a nation far more open to homosexuality in (animated) media than many in the West.
In regards to yuri fanboys, the difference between them and a guy who just thinks Girl-On-Girl Is Hot is that a yuri fanboy is interested in actual Yuri, including the Shipping aspects of the fandom, while the latter involves individuals who may never have seen a Girls Love work in their lives, so long as they get turned on by girl on girl. Fictional yuri fanboys don't show up often as a significantly greater emphasis is placed on non-shipping Girl-On-Girl Is Hot types.
Yuri Fangirls also exist, especially since yuri fandom itself comes significantly closer to gender parity than its yaoi counterpart. In fiction, Yuri Fangirls are a popular character type within Girls Love series.
Yuri Fan is for shipper examples. For non-shipping examples who still love seeing girl/girl action, see Girl-On-Girl Is Hot (although the two tropes can overlap). Not to be confused with fans of Lowenthal, Lowell, Sakazaki, Volte Hyuuga, Petrov, that creepy fellow who failed to take over the Soviet Union by mind control back in the '70s, the first man in space, an ex-Spetsnaz soldier, or a 3WA Trouble Consultant... well, there can be some overlap with that last one.
- Satoshi Furutorisui from Secret Of The Tripower. Constantly taking pictures of girls when they're together.
- Tsumugi Kotobuki from K-On!, is this. She frequently has daydreams whenever two girls are holding hands, standing close to each other, and at one point is openly jealous of the skinship between the other girls... But much less so on the anime.
- Pictured above: Hiyori Tamura in Lucky Star. She is also implied to be a Yaoi Fangirl but it is never elaborated further in the series.
- The all-girl high school in Otome Kikan Gretel seems to be populated by yuri fangirls, who Squee when they watch Mariya and Yuu kiss. But then again, they are all implied to be Schoolgirl Lesbians, as well.
- The girls from Mariasama ga Miteru often seem to be rather interested in the amorous entanglements between other girls at their school, although this is rather downplayed in the anime. In the Light Novels, however...
- Yurina from Hana no Yurina Gumi in one Yuri Hime S anthology is a very obsessed Yuri Fangirl. She goes to an all girls school and as president of the school's literature club, she writes fiction pairing up some of the students. She's also been known to Squee and gush quite loudly when two female students touch their hands together.
- Ushio's brother, Norio from Sasameki Koto, who writes Girls Love novels.
- In Haruhi-chan, Yuki Nagato is a yuri fangirl. Yes, really. In the original, she seems strangely interested in shipping Haruhi and Mikuru together.
- Onsokumaru and the ninjas of Ninin ga Shinobuden are pretty perverted but they've also been seen to cry over the relationships found in a parody of Mariasama ga Miteru.
- The Kannazuki no Miko audio drama reveals that Himeko's favorite manga is a Yuri doujinshi.
- Itta from Girl X Girl X Boy doesn't start out this way, but he becomes a yuri fan later in the manga. He then can't help but smile and go "Aww" when he sees two females acting friendly towards each other.
- Yuru-Yuri has the yuri fangirl Chitose who frequently imagines Kyouko and Ayano together in both relatively tame and explicit situations often resulting in her getting a Nosebleed.
- Amusingly, she can only do this when she takes off her glasses. So she's an inversion of Shipping Goggles!
- The students at the all-girl high schools in Aoi Hana show several levels of fascination for girl-girl relationships. The news club of Akira's school, Fujigaya, even publishes rumors about them on the front page of their school magazine. Akira is not amused, even if they don't mention her or Fumi by name.
- Hayate from Hayate Cross Blade has her yuri goggles permanently on. She sees yuri everywhere.
- Sunohara in Clannad was overloading with hormones when he and Tomoya tricked Ryou into thinking that Nagisa is going to confess her love to her, and the entire thing started playing out like something straight out of a Girls Love anime.
- Saito of Zero no Tsukaima. He got amused at the sight of Louise and Tiffania groping each other in the women's bath. Also, he got turned on when he saw Montmorency and Beatrice kiss while under the influence of the Love Potion.
- Fukuyama of Girls Bravo set up an all girl wrestling tournament and was especially excited about seeing Kosame and Kirie mud wrestle each other.
- The Yuri erotic game series Sono Hanabira ni Kuchizuke wo is predictably full of these. Whenever a group of girls witnesses a Yuri act, just like clockwork, many squees will be heard.
- Tedd, the Mad Scientist from El Goonish Shive has an interest in gender bending pretty much everybody in every way but with a notable love for girl and girl.
- Reynardine of Gunnerkrigg Court once asked Annie and Kat if they were gonna kiss because he wanted to watch.
- Ume Aoki
- Kunihiko Ikuhara
- Miyabi Fujieda
- Sappho, and thus this trope is...
- Joss Whedon
- Yuki Kajiura
- There's actually a good number. These are only the more notable ones.