Bug introduced in 8.0 or earlier and fixed in 9.0
I have:
Assuming[-nn <= m <= nn && m ∈ Integers,
Simplify[Sum[KroneckerDelta[m, n] f[n], {n, -nn, nn}]]]
And it gets me
$$\begin{cases} \mathtt{2\,f[0]}&\mathtt{m}=0\\ \mathtt{f[m]}&\mathtt{True} \end{cases}$$
Do you know why there's a factor of two if $m=0$?