To start with, I think you all might have run in to the big problem of Teemo. Teemo is supposed to be good against melee champions because of his kiting ability. But sometimes I feels that he is bit OP. There were times I failed with my fed champion to Teemo. This situations made me analyze Teemo and think of the ways that we can counter him. I like to share what I have found. However, always remember he is very strong and extremely annoying, but not unbeatable. On the other hand, a good Teemo player can always be uncountable (buts it is very rare).
If you are not feeling like reading this, I will give a summery with several words. Long poke, Stuns, slows life pots, life steel (regenerate health), dashes (gap closers), leap and bust, build AR or MR.
With above you might have an idea about champions who can counter Teemo. You can use one of web sites on counter picks if you still cannot think about a counter. Personally, I feel that games should be able pick the counter by thinking of the abilities required. Nevertheless, if you need some names I will suggest Xin (one of my mains), Panthon, Aatrox, Kha’Zix, Jax, which I have tested and worked (I feel that you can see a pattern in my selections, they all are leap and bust type). There are some suggestions like Yorick, akali, etc. but I have not tried so I cannot give any comments on them.
Beware of blind (target will miss auto-attacks), it can ruin your combo. Always try to have a combo that can stun/slow + damage bust. Like Panthon’s W + E. You might need to try items that can give you temporary shields. In addition, remember, this will not hurt much in mid and late game.
This can be very irritating late game. A good Teemo will place them nicely, so you won’t get away from ganks. Nevertheless, there is a problem in most of the Teemos, seems to place them in bushes so run in obvious paths not in jungle.
Know his weaknesses
He has a job in his team, it is to kite you and place mushrooms in the whole map. Because of these Teemo can’t get last hits on minions like you. A good Teemo will try to attack you as soon as hid Q cools down. Know his cool down and leap as soon as he tries to approach you. He has a low range and use that. He is very squishy and his short attack range makes him vulnerable, and his intension to poke you always make him an easy gank.
All of these tips are tried and working. However, as I mentioned before, as a Teemo player I myself know what you are trying against me and will try to counter that. Think that you opponent knows what you are going to do. Still you can do it but do not be high predictable on timing. There jungler might be waiting for you. Hope this give some good tips. Good luck with counting Teemo.