I'm just waiting for everyone who's in shameful, shameful denial that Korra and Asami are an item. I'm basically preempting this response for inevitable posts about this.

Because if that ain't the look of two people in love, I don't know what is. I don't know about you, but I don't just hold hands with anyone while saying that we should go on a private vacation, just the two of us, while staring into each others eyes. (While yes, going in for a kiss would've been nice, homosexuality is considered illegal in some countries that the show airs in, so that may have caused problems there. Plus Nickelodeon is full of ignorant shit-bags.) But anyway, honestly, there was a lot of build up to it. I mean, the reason Asami and Korra both had struggles with Mako, to me, is that there wasn't really a friendship built as a solid foundation. For them, the relationships were just sorta jumped into willy-nilly, because "it felt good at the time." But Korra and Asami had a friendship built over time. If you paid attention, they grew closer and closer, to the point that Korra didn't even trust anyone else but her, at one point. That's how good relationships blossom. People talk about wanting them to just be close friends, but guess what- your partner should be your best friend in the first place! Otherwise, what the hell are you even doing with them? The most successful relationships I've seen, the people I've seen get happily married and/or happily living together were all really good friends before dating, or at the very least, learned to become best friends before putting a ring on a finger.
I know people will think they were strictly straight and that this is purely platonic because, "Well they like boys, they dated Mako." Discovering your own sexuality and how you feel about certain people is a growing process. Some people feel completely set in stone from the get-go, but a lot of people spend a good chunk of their lives questioning how they feel. I'm friends with plenty of both. With Asami as someone she was close to, especially since she'd never really had any girl friends before for the past 16 years of her life, that could've very easily led Korra to consider feelings she'd never thought about before. Or maybe she always felt open about who she could fall in love with. Either way, there's no cut-off date to think about how you truly feel about yourself and/or another person.
And besides, who ends an amazing series with two people intimately standing together, alone, in a gorgeous atmosphere following an incredibly intense climax, after the most romantic kind of occasion ever, saying, "Let's be really good friends like we've already been!" Pffffffffft.
(Also I totally freaking called it when Bolin said, "You may now do the thing." Didn't know he could marry people though, that's pretty dang neato. Varrick and Zhu Li are tied for best relationship and best characters in this series.)