As the previous answer says, the Constitution has been amended 27 times, with the last one coming pretty recently. Let me give you a few more details.
The 27th Amendment says that if Congress votes to raise their own pay, it doesn't kick in until after the next House election. This is one of the stranger amendments in terms of how it was passed. It was proposed in 1789 and not ratified until 1992.
To say there are 27 Amendments somewhat overstates the number of times the law has actually been amended. The first ten amendments (Bill of Rights) were all adopted at once. So there have really only been 17 separate times that the Constitution has been amended.
One more bit of trivia, the 18th and 21st Amendments cancel each other out -- these were the start and end of Prohibition.