Ten Things No President May Do:

[MineralMan]

1. Create Any Law - Creating law is reserved to Congress by the Constitution
2. Overturn Any Law - Repealing laws is reserved to Congress. The Federal courts can declare a law to be unconstitutional.
3. Act in Violation of Any Law - A President is bound by the existing laws that have been passed by Congress and have not been repealed.
4. Spend Money in a Way Not Appropriated by Congress - See #1 & #2
5. Selectively Veto a Portion of a Bill - There is no provision for this kind of action.
6. Fire any Federal Judge, Congressperson, or Senator - That is outside of a President's authority.
7. Make any Binding Treaty with another Country - All treaties and similar agreements must be ratified by Congress.
8. Create or Change any Taxation - Again, all taxation or changes to taxation must be initiated by Congress.
9. Appoint any Cabinet Member or Judge - A President may only nominate people to such positions. They must be ratified.
10.Do anything Reserved to The States - A President may not interfere with issues not expressly enumerated in the Constitution.

The above list explains why President is unable to do many of the things some expect him to do. We have a weak executive in the United States, and that's by design.

Edit: Changed "Can" to "May" in title.