A lot of people forget that Archie and Veronica were the original Official Couple; it's only because of Betty being a Better Than Canon match for him that Betty and Veronica even became a question. The newspaper comic version does a much better job of emphasizing Archie/Veronica, but this still just doesn't help at all. During the last couple of decades, the writers have tried to make the triangle more even; Betty gets about as many dates with Archie, and Veronica has several other (one-shot) boyfriends.
Which, of course, has led to Clark/Lois becoming the Fan-Preferred Couple for many - ignoring the fact that they have considerably better chemistry and work on more levels than "both really strong heroes," most people LIKE a humanistic, down-to-Earth Superman, and consider him being Happily Married to a normal (albeit talented) human to be a major factor in that.
Some fans, however, are drawn to the differences of Superman and Wonder Woman when pairing them together - Superman was raised in the heartland of America with blue collar values while Wonder Woman was raised by Amazons, who were basically the female equivalent of the Spartans, and is royalty to boot. The differences of their ideologies and upbringings, however, is not always mined as well as it should be.
Batman/The Joker. Oh. Ye. Gods. This is the most popular Batman Foe Yay pairing. The fact it is canon on the Joker's side helps.
Keeping with clowns, Harley/Ivy is a popular alternative to Harley/Joker given their close relationship in canon.
Almost all fans love Dick and Barbara together. They've gone back and forth between being canon or not, but usually the two are incredibly close.
There's quite a bit of support for Robin (Tim Drake)/Batgirl (Cassandra Cain). They're opposites in a lot of ways, but they end up complementing each other very well. Support for the pairing got stronger when Tim's official love interest was believed to be dead.
Scarecrow/Riddler is probably the second most popular villain pairing after Harley/Ivy. Pretty good considering they had barely any canon interaction prior to the New 52.
Spider-Man/Mary Jane. Yes, you read that right. You have Joe Quesada to thank. MJ actually has more of a history of this reaction: she was—and still is—very popular with the fans, and she's been written out of the books before to have a more "appropriate" love interest brought in to be Peter's romantic partner (like Deb Whitman, or the more recent Carlie Cooper). Problem is, with the exception of maybe The Black Cat, these love interests are as dull as a rock and don't hold a candle to MJ's character. From the very start of their relationship, fans preferred Peter with MJ. If only those silly creators didn't get in the way...
If you know where to look, Peter and MJ are still very much together (the Spider-Man newspaper strip for example)
Back when Gwen was still alive and Peter Parkers's official love interest, Mary Jane Watson's unexpectedly huge popularity with the readers was a serious problem for Stan Lee and John Romita. They tried a lot of things to tone MJ down and make Gwen more "exciting," which in some respects only lampshaded their problem as it made Gwen more and more resemble MJ, most notably by changing her original hairstyle into a variant of Mary Jane's. The way Stan Lee wrote about it later, the matter was not helped by the fact that he himself found Gwen less interesting than MJ...
And speaking of the Black Cat... you guessed it! Outside of the core MJ/Gwen/Felicia trio, it seems that there are few women that fans would mind pairing Webhead up with. And a sizable portion of them hail outside of the Spider-Man comics (i.e. Jessica Drew, Carol Danvers, etc.).
In The Mighty Thor, the mightiest pairing is easily the Foe Yay/Ho Yay/Not Blood Siblings-Yay of Thor/Loki. This is most likely because they're the two most established characters in the series, and have a few really heartwarming moments that the shippers run with. Plus, on the het side, the Thor/Jane (or Don/Jane, it's gotten confusing) Thor/Sif, and Thor/Amora shippers are too busy fighting with each other to deal with Thor/Loki shippers. Even though it's canon, most people regard Doctor DoomxLoki as a joke.
Loki originally had a wife, Sigyn, to match with mythology. She vanished due to Chuck Cunningham Syndrome, since she really did nothing except help Loki occasionally (and stop helping him just as much when she realized he was evil). No one really thinks about this now.
Balder's most popular pairing is not with his actual Dating Catwoman interest with Karnilla, but with Loki (probably because Karnilla only ever shows up when needed for very specific plot, so like Jane and Sif she doesn't get much panel time).
Official Couple Kelda and Bill are popular with each other, though. Probably because no one had heard of either before their arc.
In the Thor movie fandom, however, Thor/Jane is much more popular (probably due to the whole Donald Blake Sharing a Body issues not being present) but Thor/Loki is still very strong, with Loki's main other choices being Tony Stark on the Ho Yay end and Darcy Lewis or Sif on the straight end. Most of the competing ship's stories are fairly similar in number though.
Thor/Loki still beats out Thor/Jane by a very large margin, however. Thor/Jane's biggest competition comes from Thor/Sif, which might even be more popular than the aforementioned couple.
It should be noted though, that even with a few clashes, most Thor fans seem respectful of other couple choices and there isn't too much Die for Our Ship or Ship-to-Ship Combat. Weird for a Comic Book, but that's not a bad thing.
Many fans prefer Invisible Woman to be paired off with Namor rather than her own husband. Considering the playing-up of Mr. Fantastic's neglectful side AND having Sue and Reed be on opposite sides of the Civil War, it seemed like a distinct possibility. (And, not surprisingly, it didn't happen. But they did tease us with it a bit.)
An interesting situation occurs in the Knights of the Old Republic comic since many fans wanted Zayne to hook up with Jarael instead of his more obvious love interest, Shel. The reason this is an interesting situation is because Zayne and Jarael become a couple in the last issue, thus making this a rare example of the Fan-Preferred Coupleturning into the Official Couple.
Wolverine/Jean Grey, anyone? This originated when Wolverine was a new member of the X-Men, and had yet to establish himself as the Ensemble Dark Horse. Creating a love triangle with him and the existing Cyclops/Jean Grey couple was in large part to flesh out and draw interest to a then-unestablished character, but the Wolverine/Jean pairing (and Wolverine himself) became far more popular than the creators could have imagined.
In spite of the fact that Storm and Black Panther are officially married, Storm and Nightcrawler remains very popular among the fans. This may be in part due to the popular opinion of much of the fandom that the Storm/Black Panther relationship is a badly-written case of both Token Minority Couple and Strangled by the Red String.
Seems like the writers realized this, since due to the events of the "Avengers vs. X-Men" story arc, Black Panther annulled his marriage with Storm.
X2 contributed a lot to this, as Storm and Nightcrawler had a scene that was borderline Ship Tease.
Another popular pairing for Storm is to ship her with Logan. Fans of the pairing cite that Opposites Attract, and that her reserve and idealism would balance out his Anti-Hero tendencies, while his more earthy, passionate nature would keep her stable and grounded.
Wolverine and Storm as a married couple have actually appeared in the X-Men animated series in one alternate timeline. Alas, they had to give their relationship up to Set Right What Once Went Wrong, but Professor X still remembered them and it was implied he'll try to play matchmaker. Pity the show didn't last long enough.
It really doesn't help that in Uncanny X-Men, there was a Wolverine/Storm/Nightcrawler Love Triangle going when out of nowhere Reginald Hudlin decided that the two most prominent black male and female Marvel characters had to be together regardless of trivialities like near-total lack of interaction and what it means for their individual stories.
As of Wolverine and the X-Men #24, Wolverine/Storm is canon.
Don't forget Cyclops/Jean Grey, now that Cyclops/Emma Frost is the Official Couple. And reserve a spot for Scott/Emma if Jean ever comes back.
Wolverine and the X-Men is also partly to blame for a sizable fleet of Wolverine/Emma Frost shippers. Though this might have less to do with any sort of chemistry between the two and more with the fandom's collective hatred of Scott Summers. And yet, it's a ship that many Cyclops fan can unite with the haters on, because so many of them found pairing him with Emma instead of Jean to be ill-conceived.
New Mutants has Elixir/Wither, for both the obvious and the fact that their powers cancel each other. But mostly the obvious. Wither is also more commonly paired with Mercury than his canon crush, Wallflower.
Many Teen Titans fans were thrilled when Beast Boy and Raven got together. Than came One Year Later, during which they broke up. The fans were less than thrilled. The fandom rejoiced when the two finally grew up and reunited in 100th issue of Teen Titans in 2011... but then came the New 52 reboot. Shoot.