Not often. Based on an article issued by the Cornell Law School:
The first such suit occurred in United States v. North Carolina, which was an action by the United States to recover upon bonds issued
by North Carolina. Although no question of jurisdiction was raised, in
deciding the case on its merits in favor of the state, the Court
tacitly assumed that it had jurisdiction of such cases. The issue of
jurisdiction was directly raised by Texas a few years later in a bill
in equity brought by the United States to determine the boundary
between Texas and the Territory of Oklahoma, and the Court sustained
its jurisdiction over strong arguments by Texas to the effect that it
could not be sued by the United States without its consent and that
the Supreme Court’s original jurisdiction did not extend to cases to
which the United States is a party. Stressing the inclusion within the
judicial power of cases to which the United States and a state are
parties, the elder Justice Harlan pointed out that the Constitution
made no exception of suits brought by the United States. In effect,
therefore, consent to be sued by the United States “was given by Texas
when admitted to the Union upon an equal footing in all respects with
the other States.”
Suits brought by the United States have, however, been infrequent.
All of them have arisen since 1889, and they have become somewhat more
common since 1926. That year the Supreme Court decided a dispute
between the United States and Minnesota over land patents issued to
the state by the United States in breach of its trust obligations to
the Indian. In United States v. West Virginia, the Court refused to
take jurisdiction of a suit in equity brought by the United States to
determine the navigability of the New and Kanawha Rivers on the ground
that the jurisdiction in such suits is limited to cases and
controversies and does not extend to the adjudication of mere
differences of opinion between the officials of the two governments. A
few years earlier, however, it had taken jurisdiction of a suit by the
United States against Utah to quiet title to land forming the beds of
certain sections of the Colorado River and its tributaries with the
states. Similarly, it took jurisdiction of a suit brought by the
United States against California to determine the ownership of and
paramount rights over the submerged land and the oil and gas
thereunder off the coast of California between the low-water mark and
the three-mile limit. Like suits were decided against Louisiana and
Texas in 1950.