Annie's Balance: My Explanation
Greetings to all the poor victims who wish to sit through my walls of text. I am an 
main and I have read many small forums discussing Annie's balance, ranging from descriptions as to why she is balanced to why she is overpowered and worth the banhammer. I rarely give my input and decided to write my own thoughts on my own post. I am bad at introductions I think, so here is the Great Wall of Text:
Annie: In Summary
is one of the original champions of League of Legends, which is reflected by her simple (yet explosive) kit. There is little counterplay when her stun is up other than to predict when she is about to all-in and attempting to stay out of her range. However, she cannot really 100-0 you unless she is fed or until around mid-game (where she shines greatest). She might be able to burst you after some poke, even if you are playing a squishy, but 100-0 is not really common unless she is fed and/or has Ignite up and you are alone. Once her combo is over, she becomes quite fragile, and a lot less scary.
can blow up carries, but she must reach the backline to do so. If your tanks/frontline play effectively, they can make her burn her abilities (stun and burst) on them, largely decreasing her opportunity to assassinate the carries. In lane she is very strong against melee champions such as 
and 
(she can harass them and burst them easily), but she is weak against long-ranged mages like 
and 
(she usually has to roam in these lanes- remember pings and wards).
Countering Annie: My Personal Advice
In lane, you must do the most boring thing in the world: keep your distance and farm safe. Once uses her stun spell on anything, trade with her, as her power is significantly weakened. Do so especially before she hits level six, as her auto attacks are very weak and slow. Keep in mind that she will be forced to farm with her Q if she is under pressure. Thus, essentially, you must try to be the controller of her Pyromania (stun count).
After laning, you must keep your distance (as you would against 
). She dominates mid-game but she falls off late-game, as most burst and assassin champions do (full builds mean higher defensive stats and actives). If you catch out, punish her for it (while attempting to not group for a strong counter-initiation by Tibbers). Make her have to use her stun and burst on a tank, and be sure to keep track of her 
.
If her is up and a teamfight occurs while you are playing a squishy champion, position where is unable to -ult you. As stated previously, make her use her utility and damage on the tanks/frontline. If her is down, she has to put herself in danger to get close enough to hit the backline.
If you are playing an assassin, as always, you should not enter the fight until the burst and/or crowd control abilities are down. Once uses her stun (especially with Tibbers), she is susceptible to burst from high-damage champions like 
and , or even most AD Carries.
Always remember too that 
largely reduces the effectiveness of 's combo (I despite this item when I play her), and 
should definitely be used on her when it is available.
What Makes Annie Unhealthy?
In lane there is not much that can be done sometimes against , truly, despite what many mains might claim. If she has and 
up, chances are she can just +ult you and use her combo and you are dead (unless you shut her down or your jungler is there to counter her). That is what is not healthy about and her kit. This is the aspect that is widely hated by the community, I believe, that in a one on one situation, where all abilities and summoner spells are up, is just about guaranteed victory. However, it is made up for with a timeframe where she is poke-able and gankable without her summoner spells (camping an who used is a nightmare for her unless she is fed).
I know that is hated more in the support role than at mid-lane, where her power is truly exploited, because she can hold her stun forever and forces you to play back. However, the same can be stated for a select few supports, such as 
, 
, and 
(who are prepared at all times to all in you and perform very unforgivable crowd control). The difference is that their abilities are dodge-able. They compensate this with their longer range and tankiness, whereas with , her stun is (mostly) unavoidable but short-ranged. Once again, this does not make for a very fun or healthy time, despite that I do not personally believe that it is overpowered (further explained).
Annie's Cons
-Crowd control is not always up, it must be built up
-Her range is low
-She has no mobility and little effective form of engagement without
Annie's Pros -Her crowd control is easy to build up (to which can then be held onto forever, particularly in the support role- not necessarily at mid-lane) -Can nearly if not completely 100-0 most squishies with her full combo -She receives easy farm with her Q and its refunded mana (which exists for passive buildup)
Common Suggestions:
If 's ultimate was given a delay and made into a longer range (as is commonly suggested by players), then it would be very similar to 's ultimate, except much more powerful. I personally believe such a change could make her more powerful, but it would be healthy since you would be able perhaps away from the ultimate or use 
before it strikes. I am not going to say that I am rooting for this change specifically, but I wanted to mention my thoughts on it since it is highly likely it would be suggested anyway.
As for the runner-up suggestion (which is to limit her passive with a certain amount of time), I do not really like. It could fix her support zone, but harm her mid-lane, and I believe that it is just not the correct direction to go in to make her healthier.
In Conclusion:
Ultimately, Annie is given high instant burst to compensate for her weaknesses, which is what is usually focused on when her balance is discussed (and for understandable reasons, especially when you must be the one to fight her alone). Do I believe Annie is balanced? In a unique way, yes. Her abilities cannot be dodged easily or at all but she can be weakened via positioning, counterpicking, and counterbuilding. Do I think this is a healthy kind of balanced? Not necessarily. In summary, I think is balanced, just not in the most fun or fair way. And if it is inquired, I am certainly open for change if Riot ever chooses to do so for (although I never support the idea of a full-scale rework).