Time for me to jump in.
Old school:
Popeye/Olive Oyl: One of the longest running relationships in fiction. Peter David married them off in a 1-shot comic a few years back.
Mickey & Minnie Mouse, Donald & Daisy Duck: Disney's original couples who've never married. Do they really need to?
And, then, there is the friendship between Casper and Wendy. If a ghost and a witch could actually be a compatible couple, this would be a great test case.
Modern times:
Flint/Lady Jaye (GI Joe): I remember seeing them kiss in at least one or two episodes. I didn't follow the comics, so I don't know where their relationship went after the toon ended.
Egon Spengler/Janine Melnitz (Extreme Ghostbusters): On Real Ghostbusters, Janine did carry a torch for Egon, but in "Ghostbusters 2", she was flirting with Louis Tully (remember when Annie Potts (Janine) draped a leg on Louis' (Rick Moranis) lap?) as well. I didn't follow XG all that much, so I don't know how Egon & Janine finally hooked up (and perhaps married, based on what I did see?).
Goliath/Eliza (Gargoyles): To me, it was Disney's response to the live-action Beauty & the Beast which was around at the same time. My feeling was, if Goliath eventually slept with Eliza, would she be subject to turning to stone alongside Goliath come sunrise? I'm not sure.
Robin/Starfire (Teen Titans): The cartoon deaged the 80's Titans, especially Starfire, who became more of an innocent novice new to Earth. Having read the comics back in the day, I recall that Starfire fell hard--literally--for Robin virtually from day 1. She learned English just from kissing him! It took a while for them to finally hook up in the cartoon, but it was inevitable.
Kim Possible/Ron Stoppable: You know how opposites attract? Perfect example. Ron's a klutz, Kim excels at just about everything. You knew they'd eventually become a couple.
Then, there was the implication on JLU of Batman & Wonder Woman as a couple. GL John Stewart was torn between Vixen & Hawkgirl. Too bad CN & WB decided to end the series before things really heated up.
My Life as a Teenage Robot: Was it just me, or did Brad have a crush on Jenny, and vice versa?