import Control.Applicative
main = print $ fmap (*2) (1,2)
produces (1,4). I would expect it it to produce (2,4) but instead the function is applied only to the second element of the tuple.
Update I've basically figured this out almost straight away. I'll post my own answer in a minute..
The Functor instance is actually from the GHC.Base module which is imported by Control.Applicative.
Trying to write the instance I want, I can see that it won't work, given the definition of tuples; the instance requires just one type parameter, while the 2-tuple has two.
A valid Functor instance would at least have to be on tuples, (a,a) that have the same type for each element, but you cannot do anything sneaky, like define the instance on:
type T2 a = (a,a)
because instance types aren't permitted to be synonyms.
The above restricted 2-tuple synonym is logically the same as the type:
data T2 a = T2 a a
which can have a Functor instance:
instance Functor T2 where
fmap f (T2 x y) = T2 (f x) (f y)
As Gabriel remarked in the comments, this can be useful for branching structures or concurrency.