Shive conducted a Twitter survey to determine which El Goonish Shive non-canon pairing was most popular amongst fans. The result was Elliot/Justin.
Depending on you and your god, Faye and Marten from Questionable Content. Of course, one can say Dora is the better choice for the first five hundred strips, but recent events all but silenced Marten/Dora supporters.
Hannelore/Marigold evoked this reaction, especially after the author sank the ship in a strip explicitly titled "Suck It, Shippers", which just made more people aware of the pairing and thus subscribe to it.
In the Something Positive fandom, Davan/Pee-Jee continues to be one of most popular ships, despite being repeatedly sunk by the author. (His own opinion is that they could never work, but that and any amount fan appeals are trumped up the real-life woman who he based Pee-Jee on insisting that he didn't.) It doesn't help matters that the majority of their canon love interests are either jerks, insane, or insane jerks and given R.K. Milholland's fondness for twitting the more annoying members of his fanbase (as he sees them) and his general lack of concern for collateral damage among the remainder, it's not terribly surprising that the Davan/PeeJee ship sails on.
In the few years of College Roomies From Hell, there was considerable Unresolved Sexual Tension between two of the main characters, Dave and Margaret, even after they had sex. Then Mike's little sister, Blue, was introduced. Blue immediately found Dave interesting (why was not really indicated) and set out to pursue him. Fan opinion was strongly divided (but in a friendly way) as to which girl was better for Dave. Margaret was in the lead for some time, with much fanfic and general writings devoted to how and why the two would get together "properly", but plot developments in the strip have at least temporarily torpedoed that ship and Dave is now "happily" (the poor guy is the closest thing in the comic to a Butt Monkey) shacked up with Blue.
Megatokyo: Word of God places Miho/Ping squarely in this column. It remains to be seen whether Piro/Miho will end up here as well, but it seems likely.
In The Dreamer, although the official couple in the 18th century is Alan/Bea, there are fans who prefer Alex/Bea, considering that Alan borders on Marty Stu, and Alex doesn't.
Practically none of the Boy Meets Boy fans like Cyanide/Ronnie or Skids/Tybalt, preferring Cyanide/Skids. This might have something to do with the way Cyanide spends most of the comic pining over Skids, or Tybalt's tendency toward being a Jerk Ass (and sometimes an actual villain) who'll sleep with Anything That Moves. The author actually initially planned for Cyanide and Skids to hook up, but changed her mind somewhere along the line and decided to do a Writer Revolt, even outright stating to many disappointed fans that Cyanide and Skids would never get together.
The Cyantian Chronicles: In Campus Safari, Chatin has three suitors, Collin, Cisco and Twinky. There have been both forum and Shout Box debates over which guy will get her in the end. As of September 2008, she hasn't made a choice but seems to be leaning toward Twinky. There's no debate on Cilke and Chrome hooking up though; everybody likes that pairing.
The Official Couples in Housepets! are Peanut/Tarot and Grape/Maxwell, due in part to the Fantastic Racism of the setting, which frowns upon Interspecies Romance (the former couple are both dogs, while the latter are cats). However, a healthy portion of fan-produced artwork and fiction focuses upon shipping Grape with her stepbrother Peanut, for a variety of reasons (the two of them are ostensibly the main characters and share a long personal history, among other things). The author has teased this particular pairing more than once as part of an ongoing Romance Arc, which may eventually lead this couple to become Official, although they certainly aren't there yet.
John/Dave is probably the most popular ship in the Homestuck fandom. To give an example: Archive of Our Own has, as of February 2014, 2500 fan fics with that pairing despite being sunk over two years prior to that date with the still somewhat infamous "i am not a homosexual" quote, 1000 above the second leading couple (Rose/Kanaya, which, by the way, is canon).
It's often hard to tell when this is going on in Homestuck as there is a very high amount of Ship Tease and relatively few actual Official Couples. However, there's a pretty straightforward example with the post-scratch kids - Jane/Jake is clearly being worked towards, but Dirk/Jake (which was canon anyway) and Roxy/Jane are much more popular.
Hussie is aware of and may have responded to this by having Jane's confession to Jake backfire, Jake revealing he is rather open-minded (and aware of Dirk's feelings), and making "cotton candy" - the Fan Nickname for the Roxy/Jane pairing - an Ascended Meme.
A long time ago, John/Jade and Rose/Dave were pretty big. Then we learned they were siblings. This hasn't exactly stopped the fanworks, but it's smaller than it used to be.
Eridan/Sollux has the most fanfictions on A03 of any ship not including one of the kids, despite the fact that they tried to kill each other at least once.
Not to mention sometimes it's nigh impossible to tell if any ship is more popular than others.
Eerie Cuties: Even though Layla is canonically straight, fans wanted to believe she was either bisexual, or in denial, in hopes of seeing her pair up with either Brooke, or Tiffany. Of course, now that Tiff's officially made it clear that she and Layla are just friends, they're hoping there's still a chance of Layla getting together with Brooke. Even it it means Layla being taken over by Lamia's persona and enthralling Brooke to make it happen.
Sakana has Taisei/Yuudai (affectionately titled TaiDai in most cases), so much that the artist even talked about their popularity in a Lifestream. A lot of the fanart of Sakana out there is featuring those two.
Blaze/Zero are this in Two Evil Scientists. About half the pages that they appear have comments that they should hook up.
Lackadaisy has Zib/Mitzi, otherwise known as "Zibzi". This would appear to leave Mitzi's canon squeeze Wick out in the cold, but he's got a backup in the form of his maybe-maybe-not romantic tension with assistant Lacy — a well-liked ship in its own right.
There's also a good number of fans who prefer Viktor/Ivy to the canon Calvin/Ivy.