How many times can a president be reelected?
As of 2012, once.
How many times has a vice president become president in the US because the president died in office and then got reelected for president in their own right?
Reelected into a second term in 1904 The 26th President of the United States was Theodore Roosevelt. President Roosevelt was in office from September 14, 1901 to March 4, 1909. Roosevelt as Vice President succeeded President William McKinley in 1901 when McKinley was assassinated. President Roosevelt was reelected into a second term in 1904.
5 times. The Egyptian semi-presidential system (A president is in power along side a prime minister who is head of the parliament) states that once elected, a president will serve for 6 years. Mubarak first became president in 1981 when he served as vice-president and the current president was assassinated. It seems very unlikely that he will be elected again however.