Some results by Donaldson were simplified via the Seiberg-Witten invariants.

From Wikipedea: Seiberg–Witten invariants are similar to Donaldson invariants and can be used to prove similar (but sometimes slightly stronger) results about smooth 4-manifolds. They are technically much easier to work with than Donaldson invariants; for example, the moduli spaces of solutions of the Seiberg–Witten equations tend to be compact, so one avoids the hard problems involved in compactifying the moduli spaces in Donaldson theory.

See also this MO answer by Dylan Thurston.

(Added Jan 7, '16) An additional piece of information I learned today from the Zabrodsky's lecture delivered by Peter Ozsváth is about the existence of exotic smooth structure on $\mathbb R^4$. The original proof was based on Freedman theorem and on Donaldson theorem. Results based on new knot invariants such as the Knot Floer homology (and simpler combinatorial descriptions of these invariants) can replace the "Donaldson side" of the proof by a much simpler argument.

didn'tthink that the proof could be much improved, but then were proven wrong. – David Corwin Jul 9 '12 at 6:02