I am curious to see your responses and why? I feel like if riot, picked champions around the same power level as a champ, and buffed/nerfed champions down to there level, that would be easier to balance. I think some of the most balanced champions are
These champions are all mid tier, and none are so oppressive they are unfun to play against, nor can just destroy everyone in the laning phase.
You must of never met the hell that is facing a good Lulu.
Far as the topic goes. There are far too many variables to ever believe a champion is balanced. A champion is only really unbalanced when they alone start chaining how the meta is played because they exist. Like tanky supports at the start of S4 making almost every other support useless. Even though they didn't change this much for a long time.
from a playstyle standpoint at least.
Nothing he does is free value. Any and everything he accomplishes in a match is through coordination and skill.
He's easy to learn, hard to master, has a unique playstyle no matter what you do with him and nothing about him is oppressive or overkill.
He's perfectly balanced, as far as LoL champions go.
these are some champs i think are balanced
I think the problem here is that everyone has their own idea of what's balanced. Someone could take a weak champion and claim all other champions should be brought down to their level, and then it'd be balanced. And someone else could take a really strong champion and say all the other champions should be brought up to that level and then it'd be balanced. So it's really hard to say what power level all champions should be balanced to without a less vague goal than most balanced. It's just me personally that would think it'd be best if everyone were brought to about Ezreal's power level and he doesn't have anything that sticks out to me as too good or too bad about him, and has multiple different builds that all seem to have uses.
Zed is pretty fair if you know how.
probably 
, takes skill to play, pretty much all skill shots, requires combo to blow someone up(not anymore T.T, since her E was changed), has mobility on a cool down.
I also think 
though most may not agree, takes skill to outplay people, and because if you can't AA cancel, chances are you aren't gonna be able to kill people fast enough. O and 
, because if you don't know what you're doing, you will be useless all game and a disgrace to trick2g.
Although weak because of OTHER champs (mobility), 
is pretty much the closest to balanced riot will EVER get to
My general rule of thumb is "If champion X got a slight buff, what are the odds you'd see them every game?" combined with "Can this champion hold their own right now?".
probably kassadin right now even with the nerfs cuz i do think having sileces as a mage assasin is pretty op and im kinda glad they tooken that out and he is still fun to play ur a mage but ur a assasin at the same time which being a hybrid champ in my experience always makes things more interesting
these are the most balanced champions in the game
EDIT:
forgot one
People who say veigar isn't balanced deserved to be smacked on the wrist and bitch-slapped promptly
Nasus is probably one of the most well-balanced champions. Heavily defined strengths and weaknesses while consistently being a tier 1 or 2 pick up in solo queue, but not god tier. After the buffs, Renekton is clearly defined as possibly the best skirmisher against 2 or 3 opponents(you can actually 1v3 if you are fed). But it also is clear that he can't build enough damage to successfully skirmish while building tanky enough to successfully 5v5 main tank. Speaking of skirmishers, Vayne is also clearly defined and balanced around late-game 2v2s and 3v3s being her strength. She is clearly outclassed as a backline carry and laner while facing competition as a mobile ADC or tank-busting ADC.
If I were to say a champion that wasn't too balanced, it might be Jarvan(not so much that he is OP though). He is good on every team comp, strong early game, strong late game, good burst damage while building tank. His only "weaknesses" I guess are that late-game other champions can be wayyy tankier and his sustained damage is pretty bad, but his CC kinda makes up for it.
idk... oriana gets monstrous later on .- . seen shockwave alone KO a team
Soraka Mid :)
Lulu, Orianna, and Rumble are all quite good and have been being used in the LCS quite a bit from what I've seen.
IMO I'd say Ezreal, or someone about on the same power level as him, is the best balanced.
If I had to pick someone it would be some ADC. There is not really a lot of difference in most of their power levels. 
most likely one of them. They are strong but none of them really push out others, yet they all bring something to the table. I think not really relying on abilities helps adcs to be more balanced that other roles.
Obviously ZED according to Riot
