The Constitution gives the President the power to veto legislation passed by Congress. (Article I Section 7)
Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a law, be presented to the President of the United States: If he approve he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated, who shall enter the Objections at large on their Journal, and proceed to reconsider it. If after such Reconsideration two thirds of that House shall agree to pass the Bill, it shall be sent, together with the Objections, to the other House, by which it shall likewise be reconsidered, and if approved by two thirds of that House, it shall become a Law. But in all such Cases the Votes of both Houses shall be determined by Yeas and Nays, and the Names of the Persons voting for and against the Bill shall be entered on the Journal of each House respectively. If any Bill shall not be returned by the President within ten Days (Sundays excepted) after it shall have been presented to him, the Same shall be a Law, in like Manner as if he had signed it, unless the Congress by their Adjournment prevent its Return, in which Case it shall not be a Law
As part of my research I have come across two very useful books setting out the specific vetoes by each President
Presidential Vetoes 1789-1988
Presidential Vetoes 1989-2000
Vetoes of President George W Bush can be accessed here and President Obama here
A table of the number of vetoes by each President can be found here.
A CRS paper on Regular Vetoes and Pocket Vetoes can be accessed here.