Ok so I want to say Howl and Sophie from Howl's Moving Castle, but to be honest that is mostly because they are really cute in the books. So if I take it purely from anime, I'd have a different answer.
Nezumi and Shion from No. 6. I think they are just the cutest thing ever. Their relationship is subtle and sweet and I guess it's the subtlety that makes it better because their relationship develops without being purely romantic. And the way they are so different, yet still work well together is great. I think without Shion, Nezumi would just be a bitter mess, or.. you know.. just dead. (not a spoiler, this is from the first episode) I mean, Nezumi probably wouldn't have lived past the age of like 12 if not for Shion saving him. Plus, the way that Nezumi teases Shion is so hilarious. Like really, you don't see him for years and you're on the run and the first thing you think to say is "LOOK AT THAT I'M TALLER THAN YOU NOW." with that sly grin like omfg Nezumi your priorities are out of wack.
No. 6 is a dystopian story, so if you enjoy those it'll be interesting. It's also not too dark and intense. It may have some dark themes sometimes, but it's from the point of view of Shion who wants to save rather than destroy so it's pretty light most of the time. Personally I like that because I don't always want to watch shows that are super intense and that's hard to avoid when you're looking for interesting plots as well, but this delivers. And I know I say this a lot but the art is still pretty. I really don't watch things if I don't like the art so it's basically always a given. And Nezumi's hair is cool. The video to the right is of the opening song, but due to copyright any video of it is muted, so I mostly just put it there for the pretty art of it.
For the record, my second favorite couple might be Kageyama and Hinata from Haikyuu. They literally just play volleyball. The whole show is volleyball. There is nothing else, volleyball is their life. And yet they are adorable. I mean come on. HE SPIKES HIS TOSSES WITHOUT EVEN LOOKING AT THEM, THAT'S HOW MUCH HE TRUSTS HIM. HE IS THE REASON THE "KING OF THE COURT" CAN UNDERSTAND THAT THE COURT IS NOT A DICTATORSHIP AND HE HAS A TEAM BEHIND HIM. And then you know, they play more volleyball. For like 20something episodes. Adorable. And they animate the games really well. I think that it wouldn't really work if they hadn't, because it's like... They're always playing volleyball. If your animation for that sucks it's going to be offending to the eyes to watch.
***EDIT: I FORGOT I FORGOT. I'M AN IDIOT. I also love Hana and the wolf man (never named) from Wolf Children. They are so perfect together and sweet and simple and if I could have a relationship like that I would die happy. Idk where I would put that in terms of favorites, but if you haven't seen it go watch it. It is a Miyazaki level anime movie with beautiful art and animation, and it is so amazing. I'm a total sucker for sad/sentimental movies so I started crying 20 minutes in and didn't stop until the end.
No. 6 Synopsis via MyAnimeList:
In a near future world, after the last great war, most of mankind lives in a handful of city states. There, for the privileged elite, life should be perfect. But for young Shion, the only thing perfect has been the nightmare his life has become since letting a strange boy called Nezumi spend the night in his apartment.
Banished to the outskirts of the city and stripped of all privileges for helping the mysterious stranger who has since disappeared, Shion now finds himself in even worse danger as his inquiry into a new series of mysterious deaths results in his being arrested on suspicion of murder!
But even as Shion is being sent to the city's Correctional Institute, the long-missing Nezumi reappears to rescue him! Now on the run, the two young men have only one chance at survival: uncover the mysterious secrets that lie at the sinister heart of No. 6!