Forcing method used in Baker-Gill-Solovay Relativization paper and Cohen's Proof of Continuum Hypothesis Independence
For more uses of forcing (via so-called generic oracles) in complexity theory, see The Oracle Builder's Toolkit (freely available from Fortnow's homepage) by Fenner, Fortnow, Kurtz, and Li. They give a general theory of generic oracles, and show its many applications in complexity. 

If you're interested in how oracles in complexity are like independence proofs in set theory, you might be interested in the following papers:


Arora, Impagliazzo, Vazirani. Relativizing versus Nonrelativizing Techniques: the Role of Local Checkability.
Impagliazzo, Kabanets, Kolokolova. An Axiomatic Approach to Algebrization. (full version freely available from Kabanets's homepage)


For the uses of forcing in set theory, see the book Set Theory (Set Theory on Amazon) by Jech, especially Parts II and III of the book (not to be confused with "Introduction to Set Theory" by Hrbáček and Jech).