Lower bounds for constant-depth formulae?
This question has been completely resolved (up to constant factors) by a recent result of Benjamin Rossman (http://eccc.hpi-web.de/report/2013/169/).

As Kaveh points out above, a depth $d$, size $S$, circuit can be converted to a depth $d$, size $S^d$ formula. 

Rossman shows that this is essentially tight. For any depth $d$, he exhibits a function that can be computed by a constant-depth circuit of depth $d$ and size $S = O(n^3)$, but any constant-depth formula (or even a $\sqrt{\log n}$-depth formula) needs size $S^{\Omega(d)}$ to compute it. 

(Forgot to say this before: Thanks to Benjamin Rossman for letting me know about this result.)