In essence, the craft are not traveling along the trajectories predicted. In fact, they are receeding slightly "slower" (relatively speaking) than they should be; the magnitude of the observed difference is increasing, indicating that there's some sun-ward acceleration which, although very small, cannot be accounted for.
There are many possible explanations without having to revise gravitational physics. Most people put it down to either a forgotten detail of Pioneer spacecraft design (e.g. long-term outgassing) or systemic problems in how data was collected and recorded (on varying computer hardware over decades). But it remained one of the great mysteries of astrophysics.
Now it looks like the mystery has deepened! The NEAR spacecraft was launched in '96 to visit the asteroid Eros. Recent observations show that the crafts speed is off by 13 mm/sec (measured with a precision of 0.1 mm/sec). At first blush, it seems that we have an observation of the Pioneer Anomaly closer to home on a different type of spacecraft. Other mission trajectories are being studied. We might finally uncover some more clues to this puzzle!
"The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but rather, 'Hmm, that's funny...'" --Isaac Asimov