Who is everyone's favorite champs?
With the interpretation that "favorite" means
enjoy playing the most and not
perform the best with, my favorites are (in no particular order, and keeping the list to <10% of all champs because I love to play them all) Ezreal, Akali, Soraka, Mordekaiser, Janna, Shaco, Gangplank, Alistar, and Teemo.
These champs tend to have certain things in common:
Slipperyness: All of these champions except for Gangplank have a distinct habit of escaping without summoner spells when you think they won't. Ezrael, Akali, Shaco, and to a small extent Alistar all have blink powers. Teemo and Shaco can set up traps beforehand to escape when things go bad. Gangplank and Alistar can delete all CC on themselves.
Secret Tanking: This is where a player thinks they can kill me but just gets baited because I took way more than they expected. All of these champions except for Shaco and Teemo (incl. ez because I build steal/vamp) have self heals, which is tanking you don't see beforehand. Morde has shielding that quickly pops in and out over the course of a fight. Mordekaiser and Alistar have powerful burst-tank ultimates. Janna has a shield. Soraka can suddenly pop on extra armor to throw off people's estimates of how many attacks it takes to kill, Morde can pop on extra resists, and Akali can pop extra armor and MR onto herself while being untargetable between combos. I've made my LoL career on cautious play that looks like reckless obliviousness, and most of these champs make for wonderful baiting.
Supportiveness: Half of these champions can be built to strongly emphasize a support role. Soraka and Janna are so supportive they're called "supports". Teemo can be built for mushroom spam to leave slow traps all over the map and worry about AP in the late game. Shaco is loaded with CC if you build high cooldown, and Alistar has crazy rescue powers between his CC and heals. Virtually every patch in the last year and a half to Alistar, Teemo, and Shaco have been called a "buff" by most players but were simultaneously a nerf to my support-oriented builds - which get mercilessly ridiculed by teammates every goddamn time, despite being OP enough that riot needs to nerf them. I hate the internet.
Sustain: With sufficient mana regeneration and lifesteal or spell vamp as necessary, most of these champions last
forever. In the first 5-8 minutes they tend to have problems staying in lane like anyone else, but they respond a lot better to mana regen items than most champions, as they're not particularly mana-hungry except for Ezreal, but he has a quirk: his base mana is just really low, it's not that his spells are pricey. This means that mana regen items or laning with Soraka is outsize effective on him. Akali doesn't have to worry about energy nearly as much as Kennen or pre-patch Shen. Soraka is a bit tougher now that she can't give mana to herself, but if you never cast Q in the early game you can still stay in the lane pretty much permanently (this will require a fantastic AD carry last-hitter lanemate, and/or lane smite, Greed, and avarice runes to be truly effective, since you can't use Q to farm). I haven't played GP since they upped the mana on parrrley but it doesn't look too bad.