Why is the exo product formed in the Diels–Alder reaction between furan and maleic anhydride?
Great question!  It turns out that the rate of formation of the "expected" endo product is actually ~500 times faster than the rate of formation of the exo product. However, the Diels–Alder is a reversible reaction. In this case, the exo product is thermodynamically favored over the endo product by about $\pu{1.9 kcal/mol}$.

So, even though the predicted endo product is the kinetically favored product (and formed first), thermodynamics eventually takes over and the more stable exo adduct is what you wind up with. More details are given in J. Org. Chem. 1978, 43 (3), 518. What a nice example of competing kinetic and thermodynamic pathways.