The Hamburger persona is old and haggard, constantly hacking and wheezing while telling taboo anti-jokes about celebrities and a fictional ex-wife. He's also notorious for raging against hecklers in the audience, with everything from name-calling to throwing his drink (which he often spits in) in their faces (if you are not easily offended, a YouTube search for "Neil Hamburger Heckler" will produce a plethora of examples).
Here's a significantly more PG example of his antics, which includes maybe his most popular catchphrase "Thaaaaaat's my life!" - from the rock-stars at Amoeba:
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