Is the Tribute selection in The Hunger Games rigged?

As @Mathew notes, certainly the second book/movie was rigged, inasmuch as the rules were changed so as to ensure that Katniss’ name would be the only name in the girls’ bowl. The Catching Fire trailer confirms as much.

As for the first book, though, no, there’s nothing in the book or movie to imply that the selections were rigged. Not that this means that they weren’t, but it’s just one of the many details that the book and film leave ambiguous. You could argue that the quasi-rigged nature of the second book’s selection implies that the selection in the first book was likely rigged as well. But I would counter, for what purpose would the authorities have deliberately selected the original choices of Peeta and Prim? Neither one seemed to pose any threat to the state to make them worth eliminating, nor did either one seem to present much opportunity for juicy television. It’s even more of a stretch to assume that Prim was chosen to entice Katniss to volunteer in her place, as volunteers in District 12 are said to be rare; and at that point in the story, it’s unclear that the authorities would have had anything against Katniss either (or known about the potential love angle with Peeta). If the authorities had wanted Katniss in the Games, presumably they would have simply chosen her.