He has started wars in Libya, Yemen and elsewhere without Congressional approval.
He has spent money from the treasury without Congressional appropriation.
He has used agencies to pass laws without Congressional consent.
He has allowed firearms to be transported to a foreign land and into the hands of enemies of the United States.
He has harassed states for passing laws important to their well being. (from the original Declaration of Independence: For suspending our own Legislatures, and declaring themselves invested with power to legislate for us in all cases whatsoever.)
He has made recess appointments when the Senate was not in recess for the sole purpose of bypassing the consent of the Senate.
He has murdered United States citizens without due process.
He, with consent of Congress, has claimed the authority to indefinitely detain United States citizens, if in the borders of the United States or not, without due process and without right of Habeas Corpus. (from the original Declaration of Independence: For depriving us in many cases, of the benefits of Trial by jury: For transporting us beyond Seas to be tried for pretended offences.)
These are all I can think of at the moment. President Obama is not the first President to violate his oath and the Constitution but he is certainly the most blatant about it in my lifetime. He is also not the only Tyrant in our Government. Virtually all current and past members of Congress have violated their oath and the Constitution. Most of the alphabet agencies, FBI, CIA, ATF, DEA, EPA, GSA, etc., have no Constitutional authority to even exist. However, they are the most insidious. They create "regulations" that have the full effect of law yet the Constitution gives only Congress the authority to pass laws. The employees of the agencies are not elected and they are accountable to nobody. Congress has abdicated their responsibilities to the point of being irrelevant and we have done nothing to stop them. In fact, we keep re-electing the same Tyrants over and over again.
As Americans, we have a duty to uphold and defend the Constitution of the United States from all enemies, foreign and domestic. While we certainly have plenty of foreign enemies, the domestic ones are far more dangerous to our Republic. If we don't wake up soon, we will not have a Republic left and there will be no peaceful way to restore the Republic enshrined in the Constitution. We may be too late already.