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The shill gambit is a type of ad hominem and poisoning the well wherein one party dismisses the other's arguments by proclaiming them to be on the payroll of some agency. It usually goes something like this:
It's used as an argument because conflict-of-interest is a serious problem when addressing scientific issues, and especially medical issues where both lives and massive amounts of money can be at risk. There are many cases where conflict-of-interest has caused problems in the past, notably when medical trials go awry because data was covered up in order to save face and/or money, but where this gambit becomes fallacious is where such conflict has not been fully demonstrated. Indeed, when a shill gambit is used fallaciously the only "evidence" given of such a connection to a big company or government is that someone endorses a particular position - and therefore they must hold that position only because they're being paid or receiving some other deal-sweetener. Such a move is less fallacious, and can even be beneficial to make, when such conflict of interest is both demonstrated and shown to interfere with a person's judgement of the evidence.
There is further justification for some paranoia over internet-based shills as there are many online astroturf campaigns. However, such shills tend to spend their time flooding sites like Amazon.com with glowing reviews of their company's product using armies of sock puppets. When shills actually do go on message boards, they will almost never engage in debate - instead, they make one or two quick posts or perform a brief back-and-forth with a sock puppet and then leave permanently.
 Big Pharma
The shill gambit is a more general form of the "pharma shill gambit" coined by Orac of Respectful Insolence. Alties are especially prone to calling anyone who calls their woo what it is shills for Big Pharma - leading many bloggers that they wish that they were making that much money.
Orac also defined the "reverse pharma shill gambit," which is calling the altie on his connection to a company that peddles quackery. He pulled this gambit himself when he called Age of Autism out for taking money from alt-med woo-meister Lee Silsby. A similar situation occurred when people noticed that Andrew Wakefield suffered a major conflict-of-interest as he was financed by companies that had a lot to gain if the "triple-jab" MMR vaccine was revoked in favour of three separate ones.
In American politics, right-wingers will often try to discredit liberal groups by showing that they, or someone they work for, are in the pay of George Soros, while left-wingers do the same to right-wing groups by showing that they have at some point received money from some corporation or other; at present the Koch brothers are popular "evil capitalist pig" figures for this purpose (Richard Mellon Scaife is so '90s, and Rupert Murdoch was '00s news.).
Conspiracy theorists also love the shill gambit, though "shill" is often replaced with "operative" or "(disinformation) agent."