I'm curious for which champs do you like more for the different position in LOL, for me they are:

ADC: Ezreal, Corki, Draven.
Solotop: Jayce, Darius, Jax.
Jungler: Lee, Hecarim, Nocturne.
Mid: Khartus, Twisted Fate, Lux (Soraka is very nice mid too)
Support: Lulu, Sona, Soraka (maybe Nami too?)

Those are my favorites, for ADC i like champs that has nice poke and escapes, for Solotop i like big damage, for Junglers the mobility and clear time plus providing a nice gank, Mid i like champs that has a nice CC, preferibly with silence, although damage wise Brand is better at spamming spells and does crazy damage, but the CC's are invaluable and finally for support champs who can protect and enhances the AD carrier.

I'm curious for your top 3 champs in LOL and why =)

PS: English isn't my mother language so srry for any bad written word.

for me its
(for the most part in order from best to least fav)
top: irelia, riven, olaf (strong 1v1)
jungle: shyvana, amumu, hecarim (initations are very good)
mid: ahri, karthus, orianna (easy to help other lanes by fast pushing and high mobility, or pressing r)
support: janna, sona, soraka
adc: varus, caitlyn, vayne

these are just the champs i do best with, i havent tried every champion, but ive played most of them, thats my opinion, but i dont win every game haha

adc-vayne/graves/nobody(only play those)
support-sona/alistar/lulu
mid-katarina/orianna/ahri
jungle-nocturne/shyvana/lee sin
top-irelia/renekton/riven

Solo top: Mordekaiser
Mid: Mordekaiser with party cap (rabadons)
Jungle: Rammus, Mordekaiser with smite
Support: Mordekaiser while drunk, Shaco, blitzcrank
Adc: Missfortune, Mordekaiser if i was way drunk and grabbed the wrong runes mystery

Top: Teemo, Olaf, Nasus
Mid : Mordekaiser, Soraka, and Sona
ADC: Twitch, Tristana, Caitlyn
Support: Taric, Sona, and Heim
(I don't jungle.)

Top- Urgot, Kayle, Shyvana (hopefully Elise)
Jungle- (never good in first place) Nocturne, Shyvana, bugger all
Mid- Lux, Ziggs, Orianna
rADC- Draven, Urgot, Sivir
Support- Lux, Lulu, Orianna

Urgot: I think of him as a ranged tank rather than an AD carry but he's still a laning anti-christ
Kayle: I love her flexability and dat ult
Shyvana: she's fun but can't find a good spot in the meta without CC
Lux: hard to stay mad when she says "stay positive"
Lulu: more or less same as Lux just purple
Ziggs: favorite champ of all time, he can farm like no-ones buisness, and favorite playstyle
Orianna: so far I'm among the few Ori support players, she can protect the Carry better than Janna for sure and still be good as a mid too, I guess
Draven: best ADc of all time
Noctune: 3rd champ I've gotten only competent jungler I can use
Sivir: just because she counters Blitz/Leona flavor of the month kill lanes
with special mention to Zyra

Top: Nidalee, Kayle, Darius (Teemo for counter pick)
Mid: Ahri, Mordekaiser, Katarina (Also Oriana)
Jungler: Nocturn, Olaf, Lee Sin (Amumu if not banned)
ADC: Graves, Ezreal, Vayne
Support: Taric, Sona, Soraka (The other favorites get banned: Ali and blitz)

In order of most to least favorite
Solotop: Garen, Jarvan, Riven
Jungle: Shyvana(Manaless ftw so my mid can be a boss), Hecarim and Udyr tie for #2, Nocturne.
ADC: Vayne, Draven, Ashe
Mid: Viktor, Morgana, Xerath
I don't play support but when I do it's Janna and only Janna.

I'd also like to throw in Kog as a special mention because he's not really ADC but I play him in that slot. He is my #1 bot pick.