In the one-dimensional case the Langlands program is equivalent to the class field theory and the two-dimensional case implies the Taniyama-Shimura conjecture.
I would like to know: are there any other important consequences of the Langlands program?
There are many, many consequences of the general Langlands program (which I'll interpret to mean both functoriality for automorphic forms and reciprocity between Galois representations and automorphic forms). Some of these are:
The Selberg $1/4$ conjecture.
The Ramanujan conjecture for cuspforms on $GL_n$ over arbitrary number fields.
Modularity of elliptic curves over arbitrary number fields. (Indeed, Langlands reciprocity is essentially the statement that all Galois representations coming from geometry are attached to automorphic forms.)
Analogues of Sato--Tate for Frobenius eigenvalues on the $\ell$-adic cohomology of arbitrary varieties over number fields.
Langlands functoriality (base change for $GL(2)$) implies the virtual Haken conjecture for closed arithmetic hyperbolic 3-manifolds. More specifically, it implies that an arithmetic hyperbolic 3-manifold admits a finite-sheeted congruence cover with positive first betti number (which in turn implies that it is Haken). The reference doesn’t really give this statement explicitly, but only proves it in some special cases. I think it is known to the experts that functionality implies the general case. The proof of the virtual Haken conjecture for hyperbolic manifolds is not known to provide a congruence cover with positive betti number of an arithmetic manifold.
