Hey!
I'm a new Rioter who just joined the Skins team.
I figured, what better way to get to know you all then by asking what your favorite skins are (and why)!
I'll start things off.
I'm a big fan of Arcade Sona, because I love super bright and colorful designs, so naturally, I was drawn to the splash art. I love the 8-bit sounds and VFX in-game ~ and getting to play with her slamming away on an arcade stick is pretty rad, too!
-KT
I love Dragon Trainer Lulu because of her dragon! I like when Lulu makes a joke, taunts, dances or laughs, the dragon does too! 
For me, skins are all about providing a different and interesting feel for the champion. I don't care about splash art, and I don't even much notice model or texture changes. Particles, sounds, and animations are what control the feel of a skin, and so that's what I look for in the skins I buy. Here's some I think are pretty good:
And some thoughts on ones I don't think work as well as they ought:
Probably Unmasked Kayle... She's my favorite champ, and that was my first ever skin. <3
Though I'd do unspeakable things to get a Crimson Kayle skin... Or a six-winged fiery one...
I have to go with Spellthief Lux, because it's the skin that fits Lux the most, despite being one of her launch skins.
The sad thing is that all five of her skins are meh at best, despite Steel Legion being "higher quality", because SLL is very dull, and not fitting of Lux's in game personality, not to mention her third military skin in a row. The other skins either just bad in model, (Commando/Sorceress) or theme (Imperial/Steel Legion).
Btw, is there any news you can give us regarding the skin that Lux is supposed to get? In case you aren't aware, a year and a half ago, in response to the negative reaction to Steel Legion Lux, Morello said that there would be another Lux skin eventually, and since then, a few champions have received two skins.
Popstar Ahri!!!! I love the pretty pink particles and model and the sparkles on her tails and the theme in general is amazing. Not to mention her recall and dance!
Most of my favorite champs are the outlandish, inhuman ones, and that generally translates to my skin choices as well. Void Fizz made me particularly happy, as did everything about Vel'koz when he released. Hazmat Heimer is also looking swanky, despite mystery gifts landing me with every skin he has up to this point already :P ( I don't know why, but I've always loved the look of gas masks. Apocalyptic Brand and Hextech Singed were also very nice in that regard!) And, like most people, I love me some fancy top-hats, so I have a soft spot in my heart for Magnificent Twisted Fate and Superb Villain Veigar, though Bad Santa is also pure gold :P
As far as sets of skins go, I've made it my goal to collect all of the Robot skins, and I've yet to be disappointed in anything that's come from them. All of the Battlecast and Mecha Skins are just beautiful, Full Metal Rammus's Powerball and ult are so much more intimidating than base, all that jazz... If I were to complain about any of them, it might be that Battlecast Xerath doesn't mesh well with the rest of the skins in the set, but I've seen that brought up more than a few times around here, so I doubt it's new information to you people on the Skins team!
And now for skin ideas, because I'm sure you don't have enough of your own already and this seems like a worthwhile place to dump them! I'll try and avoid concepts I've already seen from other people, particularly if Reds have commented on them in the past.
Jurassic Skarner: Because we already know (or at least assume) that the currently-lacking Void champs will be getting their entries into this set some day down the line, why not show some love to others who fit the mold? Skarner strikes me as a prime candidate for something almost like a Trilobite, still partially fossilized with some parts of his body more indentation than physical remains. Doesn't strike me as something that would specifically need unique particles in any way, but like his other two skins, it's far more interesting than a recolor!
Janitor Fizz: Perhaps a tie-in to the Jurassic skins? Giving Fizz a mop (and the requisite Scruffy-esque mustache, of course) is a small enough change, but then make Chomper a megalodon skeleton and everything is awesome and right with the world!
Mad Chef Shaco: I know the guy's slated for a visual and mechanical rework so I can't speak to any specific effects, but if he retains his dual-wielding ways, it just seems obvious to give him a carving knife and a cleaver, matching bloody chef's hat and apron, and possibly a terrible French accent.
Prickly Rammus: Apparently Blitz matched him correctly, as Rammus' offspring is a living, walking cactus in the shape of an armordillo! Cacti and bramble bushes sprout up around him when he ults, and he leaves a small trail of cactus blossoms in his wake as he powerballs around!
Haunted Pantheon: Something I've been surprised hasn't come up much in the past, but the Faceless Spartan just seems like the perfect candidate for a skin slating him as a possessed suit of medieval armor, decked out with a flamboyant tower shield and halberd. Depending on how much you played up the ghostly visual effects, I imagine there would be plenty of play-space available for fun animations and particles.
Cataclysmic Xerath: A walking (floating?) apocalypse. Literally a swirling vortex of death and destruction given partially-human form. Q is lightning bolts, W is erupting geysers of lava or steam, E is hurled debris (bonus points if they're mooing cows a small percentage of the time), and R calls down meteors from on high to bombard the unworthy!
Mafia Jinx and Arcade Hecarim.. although I'd love to see a new Jinx skin!
I personally would love a new 
skin I would prefer a justicar/arclight/angelic type skin since it's fitting to see him as a light sided and uncorrupted like justicar Aatrox and justicar Syndra. Also a reaper or mehca would be sooooo badass
Guqin Sona, Queen Ashe, Spellthief Lux. I looking at traditional style clothes and the Guqin skin really plays well with Sona's model. I'm a fan of blues and purples so I was drawn to the Queen Ashe splash in that manner (as well as how she was more fully clothed), but don't like how the face was drawn. I love how well her skirt is animated in game as well. I'm a huge fan of Lux and I think hoods are bad@$$, and I thought the Chinese splash was cool for spellthief (US not so much though I hope that it will be updated eventually).
Hi KateyKhaos! My favorite skin is probably SGU. Just the amount of detail and work put in not only to his model but the vfx, sound effects and champion interactions. Also the 'package' how he was presented as a whole: the comic, client animations, splash art, icons, banners. Speaking of ultimate skins, is there one planned for this year?
