As others have noted, this sort of thing is commonplace in analysis. The best results often flow directly from the strongest available estimates, and the strongest estimates are often complicated and inaccessible to the non-expert.

In more algebraic areas, you may want to look for famous results that people call "lemmas" rather than "theorems." People tend to call a result a "lemma" if it doesn't look like something you'd be interested in for its own sake, but is nevertheless useful for proving other things of interest. Now, if you are only interested in results that are deep or difficult, then not all lemmas will qualify, since some are very simple (Schur's lemma, Zorn's lemma, Yoneda's lemma) and others are non-trivial but not too difficult (Nakayama's lemma, Hensel's lemma, Sperner's lemma). However, there do exist "high-powered" examples such as the fundamental lemma or the Szemerédi regularity lemma.