Besides buying a f*ckload of wards.

Phreak said on the spotlight "some champions counter fiddle, etc"

But I can't come up with anyone who really counters him.

Also, can his ult be interrupted by any ability like silence, suppresion, etc. I know stuns dont work

Crowstorm can only be interrupted while he's channeling. Once you hear CAWCAWCAW, it's too late to stop.

Champions who counter him include anyone who can force him away from the team, such as Alistar (headbutt) or Janna (Ult). He's also very vulnerable when silenced, so characters like Kassadin and Talon who have a silence and a gap closer will mess him up if he isn't able to fear them. He's also at a disadvantage against characters who outrange him (Xerath, Caitlyn, etc.) if he can't sneak up on them.

I know that a lot of Kassadins carry cleanse ( at least those I face, perhaps I am just playing at a very low skill-level), they are very annoying to face as a Fiddle, due to the fact that they are all over the place, cannot be feared, and they shoot Null Spheres all over the place.

Specifically I'm asking in a teamfight, not in lane or 1v1.

Janna seems a great way to counter his ult, I like that. Any other champs that can do the same?
Alistar can do it but he seems to get hit by it anyways.

to counter fiddle is all about disabling his use of crowstorm. if he cant use it, he cant do much damage to a team. only drain a single target.

so the best counters are those that manipulate where he is. basically anything with a "push" effect, so as mentioned above, alistars headbutt, janna's ult, vayne's condemn, gargas's ult, and theres probably many more

also stuns do work, but not in the way your thinking of it, you can stun the fiddle and that'll stop him from moving, everyone in the radius should already be trying to put distance from themselves and the fiddle so the stun will help get you out of there without him following.

and last, everyone should have some form of MR against a fiddle, not getting it is just suicide, theres tons of types of MR items and theres bound to be 1 to fit in your build, if you think that your build has no room to fit a MR item, then your clearly doing it wrong. there is not 1 champion that doesnt have room for flexibility and thats the only way any champion should be played

When you're going 1 v 1 versus fiddle, you need to make sure you can cancel his drain. Do as much damage to him while you're out of it. Make sure you can kill him before he brings up another one. Igniting him during or before drain will also help a lot.

blitz is the largest fiddle counter alive.

if you can silence or stun before he ults, that is the true counter, but like you said, hard to do w/o a ton of wards.

once he ults, a hard counter is essentially knocking him away. so heroes like janna, lee sin, alistar, gragas. to a smaller extent, tristana & vayne (since they usually have very little health and are focused). a soft counter would be blitz by essentially sacrificing urself for the greater good of the team.

as per darkendragon, it is not possible for all heroes to buy a FoN or BV, but it is almost a requirement for every hero to pack merc treads if there is a fiddles in the game (yes, even AD support)

^^^ what those guys said

Blitz counters well... but mostly laning phase.
Other good counters:
Alistar (ulti is a cleanse) and he has 2 interrupts (one that shoves fiddle away)
Chogath: 2 interupts and a massive damage ult that helps get rid of him when he jumps in
Lee Sin & Tristana can both use ulties to shove him away, as can Jana.

Alistar might be the best... cus of his free cleanse (fiddle usually fears somebody when he jumps in) and then his headbutt.

I find Rammus can counter him pretty well, or at least Rammus will stop him from wiping out your team.
He's got a defensive steroid that gives him a lot of MR which allows him to tank the ult while running up and taunting Fiddle, preventing him from moving or Draining. After the taunt, Powerball will interrupt Drain.

He also gets decently countered (outside of ult) by Ignite or other characters that have an ability that reduces healing done.

Aside from that, Alistar.