This is one of Jesus' favourite insults. He often uses it to describe the religious leaders of the day. The word that we usually translate as “hypocrites” is the Greek word hypokritai, which, incidentally, is also the word that was used to refer to actors in the Greek theatre. Not only does this tell us something about what Jesus meant by the slur—these people were pretending to be something they weren't—but it also suggests that Jesus probably, at some stage, went to the theatre.*
While this abrasive term is scattered throughout the gospels, it's mainly concentrated in two clusters:
In the sermon on the mount (Matthew 5–7), Jesus repeatedly warns people not to be like the hypocrites. Don't pray like the hypocrites, don't fast like the hypocrites, don't give to the poor like the hypocrites… The general gist is not to do good things for the sake of being applauded.
But later, in Matthew 23, Jesus really lets loose. The religious leaders, “the scribes and Pharisees”, have been asking Jesus all kinds of curly questions, trying (unsuccessfully) to trap Him in His words. Eventually, Jesus tires of this and—in front of the whole crowd—embarks on one of the most scathing tirades in the history of vituperation. Seriously, go read it. For the next couple of pages, Jesus begins most of his censures with “Woe to you, scribes and Pharisees, hypocrites!”
Some of the other ways that Jesus describes the religious leaders in His speech (and some of these may get their own post later on) include “blind fools”, “blind guides”, “whitewashed tombs”, “snakes”, “fit for hell”, and “brood of vipers”. Of course, it's soon after this incident that the recipients of all this praise start plotting to have Jesus arrested…