Jessie x James (Mushashi x Kojiri) from Pokemon were one of my first ships. Now I tend to see James as her platonic gay friend... maybe they would marry for appearance sake and then by mutual agreement, both of them would have another romance on the side.
I had several Nicktoons ships, too.
Ickis x Oblina. (Real Monsters) Based off episodes like "Smile And Say Oblina" (where he helps her when her first 'squish' turns out to be a major jerk, and how hilariously offended he was to learn that she didn't see him on the same level as other guys) it was pretty clear he liked her first. But then she gained a little more respect for him in "Where Have All The Monsters Gone?", though they still enjoy playful bickering sometimes.
She actually kisses him a few times (as a gesture of friendship) and there's a bunch of other hints ("Rosh-O-Monster", "The Five Faces Of Ickis", "Ship Of Fools", "The Monster Who Came In From The Cold") but the series ends before they go on any canon dates or anything.
I feel a little bad that I have no OTP for Krumm, his canon love interest is Horrifica ("Krumm's Pimple", "Krumm Gets A Head") but she is kinda vapid and mean at times. I'd want Krumm to be with someone nicer overall.
Helga x Harold (Hey Arnold!) I blame the "Buses, Bikes, And Subways" episode for this. They do not get alot of character focus together, but I think they have potential anyway. Also I think it's funny/cute when Harold calls Helga 'Madam Fortress Mommy' as an insult. What does that even mean? XD
Babs x Plucky (Tiny Toons) Again, it's not canon, but they're pretty funny together (such as their banter at the beginning of an episode where Plucky tries to get out of class by going to the nurse. The main plot with Nurse Elmyra being really bad at her job and Plucky getting beat up for real was less interesting than seeing Plucky annoy Babs, which reminded me of the stupid way some middle-school boys attempt to flirt.)
I guess I like pairings where 2 character have different personalities, one being more serious than the other, and arguments erupt but it's still VERY clear that deep-down they care about each other. "Belligerent Sexual Tension" seems to be the way most websites describe those relationships.
I also liked Madeline and Pepito together in the DiC reruns from the 90's, as well as Rabbit and Tigger in "The Book Of Pooh" and The Tigger Movie. Most of my comic book and anime/manga pairings seem to fit those savvy guy/energetic girl (genderflipped in certain cases with a more playful guy and a serious girl) and friendly banter patterns.
Not too surprisingly, I also shipped Brock x Claire in Monsters University! ^__^