Bumping this because I was thinking of it just now, so I'll add in my two cents. EDIT: I'm sorry, I kinda went on a rant here... oh well.
4: Fiji Airways
This livery is very unique and grabs you're attention. It stands out from the usual crowd of plain colors and flags we see on a plane. Instead, Fiji Airways decided to decorated their planes with heritage and historical callbacks to Fiji. It's nice to see an airline that represents their country that way!
3: Cathay Pacific
Cathay's livery is special, yet simple. Their new livery touches me with it's shade of blue-green (turquoise? IDK) and the elegant bird on the tail. It makes one think of the rainforests of Hawaii, the shining coast of California, or the clear waters of Hong Kong. All in all, a livery that fits the airline.
2: Alaska Airlines
Don't get me wrong, Alaska's last livery was great, but this captures my focus in a whole new way. The new livery, I feel, represents the new destinations the airline flies to with the new green and different colors of blue. The old livery's deep blue reminds me more of northern destinations, and not the new places they fly to. The livery also complements the overhaul Alaska recently went through in which they modernized the airline. And lastly, that glorious hooded Eskimo. It has been with the airline since the start, and the decision to not only keep but update him was a great one. In summary, an excellent airline that has shown the way to modernize a livery and keep it classy.
I'm not bias what are you talking about
Ah, but who could compare to you my precious!
In all seriousness, JetBlue's liveries are really cool. What makes them cool is that the airline doesn't have all the liveries in just one livery: the tails come in all different shapes and sizes, from blueberries to stripes, it's hard to find two tails alike at their terminal. Of course we can't forget the text just below the cockpit. Yes, other airlines such as Virgin America have some sort of text there, but what makes JetBlue's different is that all of them are puns that have to do with blue (ex. Fancy Meeting Blue Here), and there are no two alike. I don't know, it might just be me, but that's a whole new level of creativity and awesomeness. Finishing off, let's look at the general livery. To be honest, the livery is fantastic: it's modern, sticks with the overall theme of the airline, and is very creative. These are some things hard to come by, and it's great to see airlines like this going outside the norm.