I Ship It!!
This is not a completely exhaustive list of every ship I would ever consider in any fandom I've ever been in......but it is a list of my favorite ships in the fandoms that come to mind, so that works well enough. <3
Video Games
Final Fantasy III: Luneth/Arc, Luneth/Refia, Arc/Refia, Ignus/Sara
Final Fantasy IV: Cecil/Rosa, Cecil/Kain, Cecil/Kain/Rosa, Edge/Rydia, Edge/Edward
Final Fantasy V: Bartz/Lenna, Bartz/Faris
Final Fantasy VI: Locke/Terra, Locke/Celes, Edgar/Terra, Edgar/Celes, Sabin/Celes
Final Fantasy VII Compilation: Zack/Aerith, Cloud/Tifa, Zack/Cloud, Reeve/Tifa, Cloud/Yuffie, Tseng/Aerith, Zack/Cissnei, Zack/Reno, Sephiroth/Zack, Vincent/Yuffie, Rufus/Tseng, Rufus/Cloud, Reno/Elena, Tseng/Elena, Rufus/Reno, Gast/Ifalna
Final Fantasy VIII: Squall/Rinoa, Selphie/Irvine, Quistis/Seifer, Laguna/Raine, Laguna/Julia, Laguna/Kiros
Final Fantasy IX: Zidane/Garnet, Steiner/Beatrix
Final Fantasy X/X-2: Tidus/Yuna, Auron/Braska, Auron/Jecht, Braska/Jecht, Gippal/Rikku, Wakka/Lulu, Auron/Lulu
Final Fantasy XII: Balthier/Ashe, Balthier/Fran, Larsa/Penelo, Basch/Ashe
Final Fantasy XIII/XIII-2: Hope/Lightning, Fang/Lightning, Fang/Vanille, Hope/Vanille, Hope/Alyssa, Snow/Serah, Hope/Serah, Noel/Serah, Noel/Yeul
Kingdom Hearts Series: Roxas/Axel, Sora/Kairi, Sora/Riku
Books/Movies/TV
Avatar: The Last Airbender: Zuko/Mai, Zuko/Katara, Zuko/Jin (Ba Sing Se teahouse girl), Zuko/Suki, Sokka/Suki, Sokka/Yue, Sokka/Ty Lee, Aang/Katara, Aang/Toph, Aang/Ty Lee, Azula/Ty Lee
Avatar: The Legend of Korra Asami/Korra
Star Wars: Anakin/Padme, Anakin/Obi-Wan, Han/Leia, Luke/Mara
Harry Potter:, Sirius/Remus, Remus/Tonks, Remus/Snape, Remus/Regulus, Regulus/Snape, Regulus/Barty Jr., James/Lily, Ron/Hermione, Harry/Ginny, Neville/Ginny, Neville/Luna
BBC's Merlin: Arthur/Merlin, Arthur/Gwen, Merlin/Freya, Dark!Merlin/Morgana, Gaius/Alice
Doctor Who/Torchwood/The Sarah Jane Adventures: Doctor/Rose, Doctor/Jack, Doctor/Master, Ten/Amy, Ten/Reinette, Doctor/Romana, Doctor/River, Master/Romana, Jack/Romana, Adric/Nyssa, Turlough/Adric, Tegan/Nyssa, Tegan/Turlough, Rory/Amy, Jack/Jenny, Jack/Ianto, Jack/'Captain Jack Harkness', Owen/Toshiko, Gwen/Rhys, Anwen/Stormageddon, Sarah Jane/Alan, Clyde/Rani
Life on Mars (UK): Sam/Gene, Sam/Annie, Sam/Maya
BBC's Sherlock: Sherlock/John, Sherlock/Moriarty
Animanga
Sailor Moon: Mamoru/Usagi, Haruka/Michiru, Helios/Chibiusa, Chibiusa/Hotaru
Saiyuki: Sanzo/Hakkai, Sanzo/Gojyo, Hakkai/Gojyo
Loveless: Ritsuka/Soubi
J-Celebrities
Johnny & Associates: Kimura/Shizuka, Kimura/Matsu, Kimura/Nakai, Kimura/Goro, Kimura/Shingo, Kimura/Tsuyoshi, Shingo/Tsuyoshi, Nakai/Joushima, Toma/Yamapi, Toma/Shun, Toma/Matsujun, Matsujun/Shun, Nino/Sakurai, Nino/Matsujun, Sakurai/Matsujin, Mastujun/Ohno, Nino/Aiba, Yabu/Shoon, Hikaru/Shoon, Yabu/Hikaru
Actors/Actresses: Meisa/Maki