One of the spurious claims being circulated by the Birther fringe is that one of President Obama's first acts in office was to issue Executive Order 13489 (PDF), which they claim was intended to seal away his birth certificate, school records and other evidence that he is not a United States citizen or otherwise unqualified to be President.
However, this executive order is virtually the same as Executive Order 123283 (PDF), which President George W. Bush issued early in his presidency and which it replaced. That executive order is in turn virtually identical to its predecessor Executive Order 12667 which was issued by President Reagan. All of these orders deal specifically with the National Archive and its role in preserving presidential papers and records. The orders refer only to records generated by the office of the President during his administration which have been kept by the National Archive since that institution was created in 1934.
Starting with Reagan it has been the practice of successive presidents to keep their operating records secret until a later date when they are made public as part of the comprehensive record of their presidency. This concern over the secrecy of White House records clearly originated in the aftermath of the Nixon presidency, which explains the discussion of executive privilege in the orders in question. It's equally clear that none of these prior presidents had any interest in concealing President Obama's birth records.
However, what none of these Executive Orders have any authority over are documents which were not generated by the President's office while he was serving. They do not apply to state records like birth certificates or private records like school transcripts. The President does not have the authority to seal those records by executive order even if he wanted to, and nothing in these Executive Orders even attempts to do so.