This is more about matchups than anything else.
For example, playing against Teemo as Darius isn't unfun. It's about that little margin between Teemo range and Darius' apprehend and whoever abuses it better wins. It's quite possible for the matchup to go both ways. On the other hand playing against Teemo as Master Yi is just a completely destroyed lane, with very little chances for Master Yi to win (I assume both players are at similar skill level).
Anyway, I consider playing against champions fun if most of their matchups have a lot of interaction between players and have sufficient amount of counter play available. Oh, and also if their numbers are balanced.
Some examples: Cho'Gath, Draven, Graves, Jayce, Nami, Vel'Koz, Wukong. Those are only a few, but I feel like most of those champions have a rather big weaknesses that can be exploited by anyone (or nearly anyone) while also having strength that they can use themselves. Of course the list is much longer, but that's a few that came to mind.
What I consider to be unfun is when champion you play against feels like either:
- You have to be stronger number-wise to beat him, just because his kit doesn't allow counterplay for most of champions.
- Enemy champion have a big advantage in numbers or tools (for no reason other than picking a champion).
I'll name a few champs I consider unfun with a bit of explanation:
Huge amount of spell vamp that doesn't fit the champion at all, especially at later parts of the game. High armor for no reason.
Too high numbers on his kit (both skills and base stats) considering how much utility he have. Mostly goes for movement speed for his base stats (considering how much mobility he have in his kit, I really don't think he needs that much ms) and his ultimate base damage (200/400/600 on top of already good CC and it can be AoE).
Just waaaay too many tools in one kit (especially the lantern is the culprit here).
%Health true damage. Makes every defensive stats useless against this skill. I really think this should be physical or magical damage (with buffed up values of course, or some other change to compensate).
Free stats in form of double crit chance, additional 50 range on AA (175 as opposed to normal 125 range) and 50% free bonus armor penetration on ultimate. His W have no viable counterplay (you can't move it, it's too big to reposition yourself to the sides, blocks projectiles from every side, you can't break it... Really, all you can do is just wait till it ends - and moving through it is simply not viable in most scenarios). His E makes skillshots nearly useless on lane (as he can just E to minion at any given time). I truly believe this is the reason why he still maintains a huge ban rate even after all nerfs.
Usually there is very little interaction on this lane.
Needlessly high defensive stats (especially if you consider all that mobility he have). A lot of free AD later on in the game.
Proxy
IMO this thing is beyond anything as far as unfun goes. There is no interaction, you cannot do much by yourself (would cost you too much farm and experience) and he ends up being incredibly strong in the end. This have to go. I think that giving minions a lot of extra stats or shield until they reach the last living turret in the lane would fix it (let's say 100 Armor and Magic resist or 250+15 per 3 minute of game shield). The shield could go off just as the minions get into turret range and I don't think it would have much impact beside the Proxy Singed (or other Proxy champions). This is extremely imporant right now since Singed have started to gain on popularity again, and while I don't have anything against him in lane, the proxy one is just hell.