The fundamental lemma is an example that most believed and on whose truth several results depend. According to Wikipedia, Professor Langlands has said
... it is not the fundamental lemma as such that is critical for the analytic theory of automorphic forms and for the arithmetic of Shimura varieties; it is the stabilized (or stable) trace formula, the reduction of the trace formula itself to the stable trace formula for a group and its endoscopic groups, and the stabilization of the Grothendieck–Lefschetz formula. None of these are possible without the fundamental lemma and its absence rendered progress almost impossible for more than twenty years.
and Michael Harris has also commented that it was a "bottleneck limiting progress on a host of arithmetic questions."