Headaches and flu-like symptoms are merely the more common and benign aspects of withdrawal. In some cases (speaking from personal experience here), withdrawal symptoms can include paresthesia, akin to Bell's palsy, and vastly lowered heart rate (on the order of 20 bpm). These symptoms can appear weeks after the initial curtailment of caffeine ingestion.

This is a case which dates back more than 10 years. Baltimore and his
associate Imanishi-Kari were accused of falsifying data that was
published in an 1986 article in the journal Cell. The case came to a
head in 1995, going to the highest levels of the NIH. Eventually, in
a very political decision, Baltimore was cleared of fraud, though
prior decisions had found Imanishi-Kari guilty of wrongdoing. Despite
the fact that almost every scientist who has looked at the data
concluded that fraud and scientific misconduct was involved, the law
panel decided that this evidence was irrelevant. O'Toole, the grad
student of Imanishi-Kari who first blew the whistle by publicly
questioning the data, had her career ruined. Baltimore was pressured to
resign his post as president of Rockefeller University, and
Imanishi-Kari lost her tenure-track position at Tufts. After they were
exonerated, Baltimore became president of Cal Tech, and Imanishi-Kari
was promoted to associate professor. This case still has a lot of
people upset with the ruling.