I'll assume you haven't seen the AD: JL episode "Furious Jealousy" during which Spud's crush Stacey admits that she does like him (while still displaying some of her past aversion to him [not wanting to be seen by others, upset stomach, etc.]). Not a complete turnaround to be sure, but it does show growth on her part.
Most of my faves have been already brought up but I'll explain why anyway:
Kim/Ron - I think what made this appealing for me was the sheer growth that Ron had to display in order for him to be appealing enough for Kim to even consider him romantically. His position as her long-time best friend didn't hurt, either.
Danny/Sam - I'll agree that, near the end of the show's run, the pairing was a bit forced, but I'll attribute that to a small number of episodes being aired in a small space of time. There were occasional hints of their eventual pairing in the first half of the series and that did appeal to me.
Jake/Rose - The fact that at the start, they both liked each other but were enemies unbeknownst to them both, was really interesting to me. The first season was hit and miss until they discovered the truth. The second season's improved quality and the focus on the relationship (on and off again and again) really cinched it for me. The finale was a bit anticlimactic, though. I wish Disney had allowed the creators to do the eps they wanted to during season two--the results could have been epic, though "Homecoming" is THE most dramatic Disney episode ever.
Aang/Katara - This romance really benefitted from an epic setting and struggle. It developed slowly and was not the focus of the series in the least. The possibility of an alternate pairing (Zuko/Katara) was even more intriguing. Plus, there were other romances around, too (Sokka/Suki, Zuko/Mai).
I'm surprised no one has brought up one of my favorites--the dual romances of Jeremy/Aelita and Ulrich/Yumi in Code Lyoko. Both were born from their adventures in Lyoko and their initial struggle to bring Aelita to the real world. Once accomplished, we saw the relationships blossom (especially that of Jeremy and Aelita) as they continued to fight XANA and discover the truth about Aelita's past. Unfortunately, most of the romantic elements of the series were dropped after season two.
Lastly, I have to include Molly (Eva)/Jordan from Oban Star Racers. Jordan's feelings for Molly are clear, and only in the last few episodes does she begin to notice. His climactic sacrifice for her is only topped by the sight of him crying as Molly streaks away from Oban.
Though their relationship was examined for only the first 15 minutes or so of the film (with THE best montage/animated sequence Pixar has ever done), it was incredibly effective. And yes, I teared up quite a bit.