Personally, it's his Dark Wind and fear that gets me, not his ult. Sure, that thing can deal massive damage, but I haven't had it landed on me (unless I'm the tank, and I ran in to boot him out of my team) in a very long time. Like other people here suggested--Clairvoyance and wards work work wonder.

This.

Low level players usually don't even know wards exist, but as you move up you'll find people always use them (if they don't have something like Teemo's shrooms or Nidalee's traps doing the job already). Against certainly enemies, such as Fiddle, the value of wards goes up tremendously. (Fiddle not only jumps out of nowhere in team battles, though that should surprise no one, he is also very likely to do some jungling and go for Golem on both sides of the map, which you should not let him just get freely.)

It gets to the point where players buy Oracle's just to kill wards, in some games.

Do not commit to a fight until Fiddle has wasted ultimate.

Have your disabler snare/stun him or push him away. Gragas and Tristana work well at throwing him away. Sion or Taric can stun him to save your team from a horrible fate. Morgana can quickly snare him and shield your squishy from being Fear/Drained and killed.

Flash helps tremendously. Save it for when Fiddle is running around.

Also, Fiddle relies on surprise. Take that away, and he can't do much.

If you have an alistar you can headbutt a crowstorm as its happening and then go in close so you can pulverize the little brat so he wont do anything else.

Failing that, use teemo mush/jack in the box in likely ult charging locations