Here is a summary of proofs techniques I have seen used in sci math. Other posters are welcome to supplement this list with their favorite techniques.
1. Proof by Obscure Interpretation. Interpret a well-defined mathematical equation or a sentence in a bizarre and strange manner to arrive at a conclusion.
1a. Proof by Lack of Opinion to the Contrary. A supplement to the Proof by Obscure Interpretation.
ex. "You say that my interpretation is incorrect. Then what is your interpretation? You don't have one? Then therefore, my interpretation is correct."
1a is often used to prove the existence of god.
2. Proof by False Analogy Claiming that one's proof works just like the proof of another proof with does not remotely resemble the original problem.
ex. "My proof works just like the proof that sqrt(2) is irrational."
3. Proof by Confusion The poofer uses intentionally obscures the assumptions and uses unnecessarily confusing construction to draw a conclusion that is not even remotely related to his or her construction.
4. Proof by Blatant Lying. 4a. Proof by Putting Words into Other People's Mouth. 4b. Proof by denial.
5. Proof by convincing 30 undergraduates. Surprisingly easy if all 30 of them happen to be in the same class with you as the instructor.