Sometimes, a president will veto a bill because of the (often) massive amounts of "pork" attached to it. "Pork" is something that is unrelated to the bill itself but because it appears on the document, the president has to either accept it or reject it entirely. This often puts presidents in predicaments, for while the original bill may indeed be the "will of the people," the pork attached (often) is not.
There have been two attempts to create "line-item" veto power for the president. A line-item veto would allow the president to cut anything he finds unrelated to the bill as he sees fit. Both times it has come up before the House and Senate, line-item veto power has been rejected.
This inability to choose what passes could be seen as pro and con. If you are a senator and the bill has pork for money for infrastructure, for example, and the president has to accept it or lose the bill entirely, it is a pro. However, if he indeed uses his veto power, not only does your pork get the boot, but so too does the bill which allegedly represents the "will of the people."
Some presidents use their veto power more than others. FDR used his an astonishing 635 times. Bill Clinton, 37, George Bush, 10. As of this date, Barack Obama has not veoted any bill that has come before him. You can see the entire history of presidential vetoes here.
The major con of having a presidential veto is that it is, you can argue, somewhat undemocratic. When a president vetoes a law, he (or someday she) is rejecting the will of the majority of both houses of Congress. It does not seem very democratic to allow one person to have the power to overrule the will of the majority of 535 members of Congress.
On the other hand, the veto is a very important part of the Framers' idea of separation of powers. The Framers did not want it to be easy for any part of the government to make laws that would be too radical. The president's ability to veto laws acts as a check on the Congress and, you can argue, helps to protect us from tyranny.