I touched upon this briefly but I think I need to explain myself. I ship anything from canon (Aang/Katara), to the rare (Lancer/Saber), to the downright crack (Yumichika/Tatuski). But still have rules about it. 1 I don't get mad at people for not shipping the same things I do. 2 They have to have something in common. ( Eg Yumichika and Tatski are both good fighters, value their independence, while still being loyal to their friends.) 3 The story has to show devolpment and the two charcters cannot hate each on sight.

I used to ship Uchihacest back in the day (not one of my proudest moments considering back then I couldn't distinguish Good fic from bad). I'm really not one for incest now but some of my guilty pleasures are problematic ships. It doesn't bother me as long as there's enough context between two characters in canon to create a solid and interesting dynamic. What does bother me is when I see shippers trying to put themselves on some arbitrary moral high ground by defending and/or erasing problematic aspects of a ship.

Well, if we go by lesser-known canons, then I'm fond of Reinforce/Yagami Hayate (Lyrical Nanoha) to an absurd degree, but in very specific circumstances because there is a massive age difference that could lead to a very bad place very quickly.

In better-known canons... I must agree with the pairing of Starfire/Raven mentioned earlier.

There's also the ship of Raven/Killowatt, an EXTREMELY minor character in the animated series (he doesn't even have a voice actor), but who gets an issue devoted to his backstory in the comics, where it turns out he was a superhero in an alternate dimension, who got in some kind of trouble and called out for help psychically. Raven heard and managed to summon him into their dimension, and even when they find a way to send him back she's still psychically linked to him.

a)well-written

b)do not glorify unhealthy relationships

And by unhealthy I don't mean incest, I mean abusive relationships. Although I am very easily squicked by incest because I have a sister I am very close to. Holmescest doesn't as much because my relationship with my sister isn't like their relationship, but like, Elsa/Anna from Frozen? *shudders*

My rare/obscure/cracky/weird ships...
(warning: lots of Star Trek)

Data/Geordi - but to be honest,I only consider it rare because it's not the top pairing for Data and it should be the three that are more popular I dislike in varying degrees. (One of them is twincest and another is Data/Mary Sue.) And I'm really not sure why people don't want to ship the guys who cosplay Holmes and Watson.

Taurik/Lavelle - from the TNG episode "Lower Decks". Vulcan and human roommates - it's like a Spirk TNG ensigns AU.

Jadzia Dax/Lenara Kahn - from the DS9 episode "Rejoined". Oh gods that episode was heartbreaking. I know Jadzia/Worf eventually becomes a canon thing, but I can't help but wonder what would happen if they kept Lenara on.

Icheb/Q Junior - from the Voyager episode "Q2". Q Junior is brought down to human to punish him for being callous about lower lifeforms, and the moment when he reforms is when he accidently puts Icheb's life in danger. Plus, straightlaced ex-Borg and teenage god of mischief, how is that not great?

Jason/Nico - from the Heroes of Olympus series. Don't actually know how popular it is, but it's not canon and I don't care. Nico needs a happy ending, godsdammit, and wouldn't it be a twist if the Aphrodite girl needed no man?
(also just found their tag on Tumblr, yes I needed this)

That's all I can think of. But yes, ship what you want, just do it well.

I have a few I've never even seen people write.

Saphira/Temeraire for reasons I refuse to declare

Motoko Kusanagi/ Archer(EMYIA) because I don't know.

And that goes for Smaug/Bilbo too. It goes for any and every ship going. No exceptions. YKINMK, people, do try and remember that.

As for my own pairings, Amy/Ace is a favourite of mine. There's no fics of it to my knowledge, but I can dream. In point of fact, I do. They are happy dreams. Sometimes they are dreams in which ice cream is involved.

Also at the cracktastic end of the spectrum are the following:-

Raven (Teen Titans animated series)/Skitter (Worm)
One is a teenage girl who was subjected to a campaign of horrific bullying by her peer group, one of whom REALLY should have known better, and manages to be a hero after a false start or two. One is a teenage girl who is the literal spawn of a demon and fights against that in order to be a hero and save people, with the occasional blip. I like to think they've got a little common ground.

Hermione/Tonks
Tonks didn't die. She lives somewhere safe where Remus can snuggle her and love her and SHUT UP WITH YOUR LOGIC

Kaname Madoka (Puella Magi Madoka Magica)/Haruka Tenoh (Sailor Moon)
I didn't cover this in the previous ship because Tonks is not dead shut up shut up shut up, but I've kind of got a thing for more platonic ships that enable other ships. With this one, it's Madoka/Homura being enabled by the canon Uranus/Neptune; Haruka's guidance allowing Madoka to accept that she and Homura love each other. Which they do. You cannot prove otherwise. They will eat ice cream together and sit on some swings and it will be adorable.

Agent Wobbles (PPC)/The Sugar Puffs Monster (Sugar Puffs cereal commercials)
... I got nothing.

...but I have collected some rare or slightly cracky ships. Like Susan Pevensie (post-Last Battle) x Maglor. Because Reasons.

Also there's Lark/Rosethorn, which I shipped before I knew it was canon. (Tamora Pierce's Circleverse)

And, from the version of The Ramayana we read in Humanities class, Tara/Vibishana, 'cause they're both intelligent, genre savvy, and surrounded by idiots.

Other than this, I mostly just ship what's canon, unless it's really idiotic. Oh, and Doctor/TARDIS supersedes all other pairings.

-Aila

Bunny and Raffles (Raffles stories by E. W. Hornung): it's canon as you could get with the time period, and it's got some extremely rough patches... but part of the point is that although Raffles is not always a good person, he attempts to be good to Bunny.

Eowyn and Faramir are my favorite LOTR pairing, hands down. I don't see a lot of fic with them, though.

From Recess, T.J. and Spinelli. Actually, I don't see them as staying together romantically, but I see them as dating for a while in middle and high school, breaking up then being each other's go-to person the rest of their lives.

Teen Titans gives us the SisTP of Raven and Starfire (seriously, there needed to be more alien ladies bonding on that show,) and BumbleBee/Cyborg, which I really shouldn't have to explain, because they are the sassiest couple ever.

Oh, and Lyall/Biffy of The Parasol Protectorate,, but the entire fandom ships them. It's just a tiny fandom. Also, Madame Lefoux + I don't even know, but she desperately deserves better than her life has given her so far. She needs a strong woman who won't lie to her or attempt to steal away her son.

Chemistry and Biology: Wait, there isn't a natural sciences fandom? Too bad, I've spent my entire college career shipping them, I'm not going to change my ways now.

If we're going by the definition that "rare and obscure" means "relatively unknown". I've got my share of almost-canon pairings that nearly no one remembers and would defend them to...well, to nausea.

And while I feel like Holmescest (and a lot of other -cest ships) have a higher badfic potential because of its sensitive territory, I no longer feel so strongly against it.

I have seen a couple Mycroft-as-homophobic-jerk fics, but they aren't as popular as the Mystrade fics, so that may be an outdated observation which is, of course, not so much the case now with Season Three painting Mycroft as subtly supportive of Sherlock and John.

My opinion now is to ship and let ship, and I'll edit the BBC Sherlock wiki page to reflect that.