While Sarah's various and relatively subtle attempts to influence Ellen and Nanase (putting them together for the pictures, seating them together for dinner, and maneuvering them into sitting side-by-side on the couch) definitely qualify.
The unnamed "Star Trek fangirl" ships Susan and Elliot to the point that she shows up at the video store to ask Susan about it, rather than renting a video. And just happens to be there for Sarah telling Susan about breaking up with Elliot. Cue Squeeing.
As of the Squirrel Prophet storyline, there's Sarah and Grace shipping Justin with Luke. Also serves to illustrate the different ideas of shipping they both have.
In Shortpacked!, Robin's fixation with Ethan and Thad, even after they'd both told her they weren't gonna do it... To the point where it got a little creepy.
A little? She tried to pass a bill through Congress to make them "do it"!
A bonus strip in one of The Order of the Stick books makes Elan into this. He not-too-subtly attempts to get Hinjo and Lien to hook up, out of the belief that they need to "repopulate the paladin race". They are not amused.
Violetta: Well, the crowd's for it. Moloch: The crowd is always for that!
Zeetha apparently ships Agatha/Gil. Before that, encouraged Lars and Agathauntil he died. Her homeland worships a fertility goddess whose holy days are "a lot of fun (cha cha cha)". Why would you be surprised?
And later when Tarvek finally spat it out, the entire city of Mechanicsburg, Jaeger generals included, has a betting pool on whether he or Gil gets with Agatha. The supposed "dark horse" bet is a threesome, though apparently that's such a popular choice Vanamonde says the odds are only five-to-one against it, indicating that there are more than a few shippers out for a One True Threesome.
In turn, Tarvek apparently ships Higgs/Zeetha. Higgs's reply on this is ambiguous.
Gabby successfully shipped Tipper and Chiachi together in Namir Deiter.
Falco, on the other hand, was not so lucky — her attempts to ship Tipper and Gabby just pushed the two of them apart for a while, even before outing Gabby.
Both Hod and Loki from Brat-Halla ship Thor and Sif. Loki mostly does it to cause Thor anguish. For Hod, that seems to be a bonus.
Megatokyo: Erika and Largo seem to ship Piro and Kimiko. Yuki's friends ship her with Piro at first, until they encourage her relationship with Kobayashi.
Yuki's mother obviously ships Erika/Largo. Not that it needed help anyway.
And Yuki herself is probably the biggest Piro/Miho fangirl in the series.
Pretty much everyone in Bittersweet Candy Bowl tries to get Mike and Lucy together. While Lucy is all for it (though she hates the interference in her life, she does love Mike... probably), Mike has a long-distance girlfriend and rejects Lucy, leading to much angst. Complicated by the fact that several cast members have crushes on Mike or Lucy, but still want them to get together...
Yashy is especially egregious in this regard, particularly in the earlier strips. This is complete with viciously insulting any other girl who displays an attraction to Mike... which happens to be most of them.
PeeJee ships Davan with his current girlfriend Vanessa in Something Positive. Having coerced Davan into following up Vanessa's interest in him when he never would have bothered, she likes Vanessa and she's not going to let anyone mess up her Platonic Life Partner's happiness, especially not Davan himself.
There have been a few chat logs/memos that suggest Sollux and even Vriska ship Karkat and Terezi.
UU has apparently written shippy fanfiction about the Alpha kids, but it's unknown yet what pairings she included.
There are indications that the AR may be trying to set up Dirk and Jake (hitting on Jake and telling Roxy that because of this Jake has gotten used to the idea of Dirk being into him, encouraging Dirk to confess, admitting that he has his own plots but assuring Dirk that they don't conflict with his, stressing that Jake play server to Dirk just as he suggested would help their relationship...) but his intentions, as of yet, can only be guessed at.
Beau the angel is a smirky kind of shipper in Catena. Not only is he evidently in favor of a match between Bryony and the Grim Reaper, but he's rather smug during those moments that indicate it will eventually happen.
In what is perhaps the weirdest example of this trope, Spinnerette's bottom left hand ships her and Mecha Maid.
Velvet of Deer Me has this view in regards to her roommates Thomas and Viana. This is naturally lampshaded during the "Dog Daze" story arc when Velvet notes that not all of her matchmaking efforts have panned out, gesturing towards the two of them.
Uh, Kat and Jones from Gunnerkrigg Court , anyone? Jones, hands Andrew rose, nudges him to Parley? Kat, with that exuberant expression on her face as Andrew and Parley are about to kiss, then getting Annie out of the way as she is perpetually clueless to current affairs? Later she also pushes Annie herself into talking with Jack.