Which CNF boolean formulas blow up exponentially at conversion to DNF?
The classical example is
$$(x_1 \lor y_1) \land (x_2 \lor y_2) \land \cdots \land (x_n \lor y_n)$$
which blows up to $2^n$ terms when converted to a DNF.

Most functions have CNF and DNF complexity very large – $\Theta(2^n/n)$ if I remember correctly – and so for random functions there is no blow-up for trivial reasons.

Miltersen, Radhakrishnan and Wegener construct a monotone function which has an exponential gap.