A beautiful exercise in Guilleman and Pollack asks us to show the following generalization of the Inverse Function Theorem:
Suppose $f: M \to N$ is a map of smooth manifolds, and $Z$ is a compact submanifold of $M$ such that $\left. f\right|_Z$ is injective, and $f_*$ is an isomorphism at each point of $Z$. Then $f$ maps an open neighborhood of $Z$ diffeomorphically onto an open neighborhood of $f(Z)$.
At the risk of asking a slippery question, is this the "most general" version of the IFT, or is there one more general yet?