The Overjustification Effect put one of the most famous nails in behaviorism's proverbial coffin. It's easy to see why. Simply put, rewarding people for doing something they already enjoy can make them do it less often, under certain circumstances. On its face, this seems to contradict the behaviorist's maxim that rewards increase the frequency of behavior. However, this version of the story leaves out some important details, details which lend themselves to a behaviorist interpretation.
The classic experiments on overjustification were conducted in classrooms. Researchers gave children an explicit, token reward for doing activities they already enjoyed, like drawing pictures or solving puzzles. Then, the children were given an opportunity to engage in these same activities on their own, when no rewards would be forthcoming. The result: children engaged in these activities less often than they did before.
This effect is usually summarized as "extrinsic rewards reduce intrinsic motivation," and cognitive theories tend to focus on the intrinsic/extrinsic distinction. Extrinsic rewards are the ones introduced by researchers, usually money or some kind of token that might as well be money. Intrinsic rewards are the internal pleasures assumed to motivate behavior in the first place: entertainment, mastering a skill, producing something useful or creative, and so forth.
One problem with cognitive theories is that they infer causal factors that cannot be measured directly, factors such as "intrinsic motivation." The only real variables involved are the rewards given and the frequency of behavior, and behaviorists have described several situations in which previously-rewarded behaviors can become less frequent. As in the classic experiments discussed above, they involve predictable periods of time when rewards suddenly stop being available.
Under an interval reinforcement schedule, a target behavior is only rewarded at certain times. This produces a steady increase in behavior as reward time approaches, followed by a sudden drop when reward time is over. Typically, this drop bottoms out below baseline levels (assuming the behavior occurs naturally). This is precisely the pattern observed in overjustification experiments. 
A full behaviorist account of the phenomenon might go something like this:
- Original (i.e. intrinsically motivated) behavior was learned on a continuous schedule (i.e. it rewards itself).
- This behavior is suddenly put under an interval reinforcement schedule with a more powerful reward. Rates of behavior begin to conform to the interval schedule, rather than the continuous schedule.
- When the new reward is removed, behavior drops off exactly as one would expect from interval reinforcement.
Not only is behaviorism capable of explaining overjustification, it does so without recourse to abstract and unmeasurable variables. That's science! 
- For a detailed discussion of reinforcement schedules, see my article: The Deep Magic of Behaviorism
- Self-perception and attributional theories are valuable lenses through which to look at human behavior, don't get me wrong, but their dependence on abstract variables does make them less scientific.