So spoilers as I said in the header but in the end of Legend of Korra it was almost undeniably confirmed Korra and Asami are a couple. A major cartoon series in America has a lesbian couple and it was a cool moment. Some people out there deny it and say they are just good friends and in no way attracted to each other let me give some evidence to say otherwise.
Back in the episode "Reunion" when Korra returns to Republic City since she left 3 years ago. She, Asami, and Mako meet in a restaurant to catch up and while there Mako finds out that Korra had been writing to Asami the entire time she was gone. Mako is very upset at this news and is angry with Korra for not communicating with him. Well in the finale Mako and Korra have one final conversation and there Mako tells Korra that no matter how crazy it gets he will always have her back. Now at face value this seems like nothing but if you read between the lines and see the subtext this is Mako lashing out at Korra and Asami coming out together and then accepting it. When Mako finds out about them "communicating" he is angry but this is him dealing with latent feelins he has for Korra and possibly Asami and maybe some jealousy or societal ideals of masculinity being crushed that his two ex girlfriends are now a couple. Then in the finale he has come to grips that they are together and tells Korra that he supports them and are happy for them.
Then later when Korra and Asami have a moment together they talk about each other. Korra apologizes to Asami that she was away for so long and not returning sooner. Now Korra doesn't say to Asami but it is heavily implied by the dialogue and the tone in their voices that it is about Korra not returning sooner to be with Asami. Asami then goes on to tell Korra how happy she is to have Korra back and how she is not sure how she would deal with losing both Korra and her Father in one day. Now this line is important because she specifically says Korra not Mako, Bolin, or any other character she specifically says Korra. Her father is a given it is her father but to specifically name Korra says that she cares for Korra well beyond the levels of friend and loves her which Korra reciprocates.
Now that I have gotten through that let me movee on to the last scene. Korra and Asami are going to take a "vacation" to the Spirit World together. If you watch the scene as I put at the bottom of this article you will see that their vacation is not a vacation but their honeymoon as they wed at the portal to the Spirit World. You have to flip the scene around because the video is mirrored and originally Asami is on the left and Korra on the right. Well Korra and Asami are walking to the portal as they approach it they begin to hold hands walking to the portal. When they reach the portal they face each other and take each others hands looking into each others eyes as they go through the portal. Now look at the scene as they "walk down the aisle" notice all the spirits there they are watching the proceedings much like the guests do at the wedding. Then the placement of Korra and Asami are important to because Asami is on the left and Korra the right which are the traditional positions of the bride and groom, bride on the left groom the right. Korra is far more of a tomboy and between the two is more manly then Asami so her taking the position of groom makes perfect sense. Now when they reach the portal like many wedding couples do they face each other and take each others hands during the proceeding like Korra and Asami do as they go through the portal. The show ends not with a final battle or even the awesome marriage of Varrick and Zhu Li with possibly the funniest proposal scene ever. "Now lets go attach these flying rust buckets on to the giant smashing thing! This is how I always pictured our engagement.". But with Korra and Asami being married off by the creators as they go off into the Spirit World.