Seems like she is banned a lot in tournaments and in ranked - but when she is used how/who do you counter her with?
In Crs SYDTKOs' guide on LoLPro he says
"Cho'gath, Galio, Morgana and Ziggs but note that Cassiopeia is such a strong champion, these are just things that farm incredibly well against her without dying; there are no champions in mid-lane that 'counter' Cass."
This opinion was also shared by Dignitas' Scarra on his stream a few nights ago.
So according to the pro players, she is so strong she doesn't have a counter per say, but the best you can do is farm against her and hope she makes a mistake. Hope this helped.
Some natural AP counters are Kassadin (Not in lane) and LeBlanc. This is because they have a strong built-in flash and silence burst that can catch anyone off guard.
If you have to play against a Cassiopeia, keep your distance so you don't get hit by her poisons, if you do get hit by her poisons, she has the opening of using twin-fangs since targets affected by her poison cut twin-fang's cooldowns and increases her movement speed.
Cassiopeia does have problems if the target out ranges her, like Ziggs who can throw bombs, but fear the flash ult combo.
You will want to take boots/3pots in mid lane in order to dodge her poisons and avoid getting locked in by twin fangs.
Ahri is always a popular mid ap champion that fares well against Cassiopeia. Ahri has high mobility and skills that can harass and farm creeps just as strong as Cassiopeia. Remember, Cassiopeia can only deal out damage to you if you are caught by her poisons, so if you happen to dodge her ult, you can maneuver around with Ahri's 'R' which allows you to dash 3 times.
Some Cassiopeia players will just twin fang you without even putting poison, if they do, feel free to go aggressive on them, don't just let her harass you.
https://docs.google.com/spreadsheet/ccc?key=0Aq-068L0cPIZdHdZR3JtaXlOdTZWQjJVb3FoUVZLM1E&hl=en_US# gid=0 This is only a link from the forum, not my actual property. It is a counter chart for all champions and items that can be used beneficially against said champion. Enjoy and like the guy that actually made it.