None, only diplomats have limited immunity from prosecution in
the USA. This is referred to as diplomatic immunity rather than
sovereign immunity.
Sovereign immunity in a feature of Common Law in which the
sovereign or the state is immune from civil or criminal
prosecution. The answer to your question is then that the American
Federal government possess sovereign immunity except in those cases
in which that immunity has been waived by statute. While not
countries in themselves the constituent states of the United States
are presumed to possess sovereign immunity.
A related concept is that of extraterritoriality or exemption
from the jurisdiction of local law. This may be negotiated on the
occasion of the visit of a head of state or as part of a status of
forces agreement covering the armed forces of one nation stationed
in another nations territory.