In 1986 The Young and the Restless star Peter Bergman said, in an ad for Vicks Formula 44 cough syrup, “I’m not a doctor, but I play one on TV.” [See the ad on YouTube.] The statement seems to have been intended as a sort of legal disclaimer, a different way of saying, “Consult with your physician before using this product.” (According to poster starflyer on Everything2.com, they were required by federal authority to use the line.)
The modern usage seems intended to qualify the speaker as a non-expert at job X, but without completely removing him from the realm of credibility on subject X. If a writer puts this phrase in another speaker’s mouth, it is to give a sense that that speaker doesn’t actually know what he’s talking about. (E.g., “I’m not a leftist, but I play one on TV“.)
It is also possible to vary the second half of this sentence a little, as in “I’m not an linguist, nor do I play one on TV.”
I like how the story on this one cleaves directly to the original: “I’m not a Congressman, but I play one on TV“.
Other Xs on the web: programmer, lawyer, Christian, notes expert.
[Thanks to Mr. Verb today for the pointer inspiring me to write this post. I was feeling overwhelmed with the queue before that.]
Edited to add: This one was covered at some length on Language Log in October 2005. I have been remiss [again, argh] in checking in on snowclones there before posting there. Thoroughness turns out to be more time-consuming than I realized. Arnold Zwicky says “I am not a semanticist, though I play one at Language Log Plaza…”, which suggests that the “TV” slot may be its own variable. And the pronoun “I” can vary in the first half, at least; the second half is more fixed, as in “It’s not real news, but it plays one on TV” and “I’m not Russian, but I play one on TV”. Dr. Zwicky traces the history of the original utterance of the future snowclone through a couple of actors, including Peter Bergman, Chris Robinson and not Robert Young, AKA Marcus Welby, M.D. As far as Dr. Zwicky’s research and my YouTube searching can tell me, Robert Young did not say “I’m not a doctor, but I play one on TV”, but he appeared in enough ads as a doctor, as well as elsewhere as himself, that people remembering the ad conflated his doctor with other advertisement doctors.
The Snowclones Database 
I don’t think the original ad ever reached Britain or Ireland. When I first came across the snowclone on the interweb, it baffled me. (Similarly: “objects in the mirror are closer than they appear.”) The nearest ad was a toothpaste ad c.1989 that said “I’m not a dentist, but I recognise this: [holds up tool to camera] It’s the tool dentists use to scrape away plaque.” The speaker was just a generic anonymous TV-ad actress. I don’t know of any snowclone based on that; it had potential, but the moment passed.
I was once part of a community access TV program that did sendups of just about anything we could (and some things we couldn’t). One of our women one time as part of the taping of one show said, “I’m not an actor, but I play one on TV.” In the metacommunity we had established in the show she not only played several roles, she also played the actress that played those roles.
Blogged about in a series of postings on Language Log in October 2005: here, here, and here.
In one of the mock ads in their 1970 LP Don’t Hold THat Dwarf, Hand Me the Pliers the Firesign Theatre’s Phil Austin utters the line, “Im not a doctor, but I do look like one,” which is where I first encountered any of these variants.
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that since it would run a full 4 hours, the main qiestuon on the audience’s mind might be “To pee or not to pee?”
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Paul Shaffer once said, “I’m not a piano, but I play one on TV.” Best. Variant. Ever.