I believe it is 27, and counting.

Twenty Seven Amendment 1 - Freedom of Religion, Press, Expression Amendment 2 - Right to Bear Arms Amendment 3 - Quartering of Soldiers Amendment 4 - Search and Seizure Amendment 5 - Trial and Punishment, Compensation for Takings Amendment 6 - Right to Speedy Trial, Confrontation of Witnesses Amendment 7 - Trial by Jury in Civil Cases Amendment 8 - Cruel and Unusual Punishment Amendment 9 - Construction of Constitution Amendment 10 - Powers of the States and People Amendment 11 - Judicial Limits Amendment 12 - Choosing the President, Vice President Amendment 13 - Slavery Abolished Amendment 14 - Citizenship Rights Amendment 15 - Race No Bar to Vote Amendment 16 - Status of Income Tax Clarified Amendment 17 - Senators Elected by Popular Vote Amendment 18 - Liquor Abolished Amendment 19 - Women's Suffrage Amendment 20 - Presidential, Congressional Terms Amendment 21 - Amendment 18 Repealed Amendment 22 - Presidential Term Limits Amendment 23 - Presidential Vote for District of Columbia Amendment 24 - Poll Taxes Barred Amendment 25 - Presidential Disability and Succession Amendment 26 - Voting Age Set to 18 Years Amendment 27 - Limiting Congressional Pay Increases http://www.usconstitution.net/const.html

At the moment, there are 27 of them. The first 10 are referred to as the Bill of Rights.