Yes, indeed, there are many programs that the states have no part of. The 10th Amendment says that the states and the people retain the rights/powers that are not delegated to the federal government by the Constitution.
Some primary areas that are delegated would include defense, foreign policy, and pretty much the entire federal judiciary.
States, for example, may not send ambassadors to foreign countries, nor may they declare war.
Likewise, state courts have no jurisdiction in federal affairs or affairs that cross state boundaries.
Finally, many programs are administered at the federal level. From the spooky - the NSA, the CIA, to simple ones like the National Weather Service, and the Pell Grant Administration, the Pension Benefit Guarantee Corporation (PBGC), to even the powerful ones like the Federal Reserve (alibeit also a quasi-governmental organization), there are all sorts of programs run strictly out of DC.