I remember hearing a version of the Joel Chandler Harris tale of Br'er Rabbit and the briar patch when I was 5 or so, so the trope of the tarbaby has been with me for a very long time, as has the basic (perhaps even universal) folkloric notion of the Trickster. Take a look at these sites to test the waters:

The OED is eloquent in one of its entries for the term:

doll smeared with tar, set to catch Brer Rabbit (see quot. 1881); hence transf., spec. an object of censure; a sticky problem, or one which is only aggravated by attempts to solve it (colloq.)

(the OED also notes the derogatory connotations, which I'm sidestepping). The earnestness of the discussion from c2.com wiki isn't nearly as much fun as a wander through some of the alternate versions of the tale that Harris collected and popularized, which include Bouki and Lapin, a Cajun variant of the tale, and Enola Matthews' Creole version. Follow this up with a look at Bouki the Hyena ..and n.b. that Bouki also turns up as a character in Haitian folklore, and has been repurposed for the 21st century. Those who read French will also enjoy the challenge of Compair Bouki avé Compair Dahomey (par Pa Lindor), from a collection of textes en créole louisianais (from Centenary).

Clearly a long-time resident of the folklore landscape, 'tarbaby' also has some literary connections. Ted Hughes used the term as the title of a review article in New York Review of Books in 1965.

To explore some of the marvelous plasticity (so to speak...) of the tarbaby trope, see 'network tarbaby', and this almost-inevitable allusion to the Evil Empire from an e-mail archive:

>Finally, I congratulate the author on refusing to use Outlook, and to be 
>considering OpenOffice. Of all the risks of using Windows, none is so brutal 
>as the possibility of vendor lock-in. The author says he'll return to Linux 
>some day, and given his careful choice of open apps, I think he might stand a 
>chance. But if he starts getting stuck in tarbabies like MS Office, Quicken, 
>and other Windows only proprietary apps using proprietary binary file 
>formats, the author will need to rent access to his data forever, and Linux 
>re-transition will become an unfulfilled dream. 

...though other bits of geekery don't escape, as seen in this blog entry, which links back to the wiki entry above:

Javascript may be one of the worst tarbabies on the planet. Every shot you take at it sucks you deeper and deeper in and all you get out of it is trouble.

Richard Wright wrote but never published a novel with the title Tar Baby; Toni Morrison has one with the same title (see Tarbaby and Womanist Theology [Karen Baker-Fletcher] for commentary)

Uses of 'tarbaby' in political discourse abound. See a blog entry which includes this description of Iraq:

A good friend of mine -- a journalist who covered the Middle East for many years -- calls it "the mother of all tarbabies."

(This may be a reference to Gary North's REMNANT REVIEW [Vol. 30, No. 2 February 21, 2003], or possibly America’s Tar Baby by Clara Rising [January 24, 2002])

I'm a bit queasy to find myself citing Daniel Pipes, but his article The Tarbabies of American Politics from National Review (November 16, 1992) does establish that the term has been in national polemics about Iraq for a while:

However well the war went, Bush hardly had little time to enjoy its benefits before "Saddam still has a job, do you?" bumper stickers turned up. Not only did Saddam stay in power, but his truculence and brutality remained intact. Saddam proved willing to impoverish the Iraqi citizenry and to kill anyone-Kurd, Shi'ite, or merchant-who defied his will. To protect the Shi'ites, the Western powers imposed a no-fly zone in southern Iraq. This increased the possibility of U.S. forces again in combat against Iraqis. The war showed that even if you overwhelmingly vanquish the Iraqi tarbaby, it still sticks to you.

I'll forbear to look into gamer and skinhead [?gamier?] uses of the term, which are plentiful but not exactly heuristic.