Point Roberts, Washington, is an exclave

As explained in The Atlantic's "Cities" column (via Neatorama):

The town sits about 20 miles directly south of Vancouver, on a little peninsular tip of land, jutting just below the 49th parallel... Known as an exclave, Point Roberts is a bit of an oddity in that it’s not an island and yet it’s completely separated from the rest of the U.S...

“They’ll say ’Oh my god, how do people live here? It’s like a police state.’ And in some ways it kind of feels that way. On the one hand, it’s been rated the safest community because it’s like having a really, really, really strict security guard gate..."

Further discussion at the link, where it is noted that -

...the town is, unofficially, home to about 50 people in the U.S. Marshals Service’s Witness Security Program, or Witness Protection. Other residents have come here seeking their own protection.

Wikipedia has a nice page listing and explaining "exclaves" and "enclaves." A nice example of a "sub-national" exclave/enclave is Kentucky Bend:

And newbies to this blog who want to read even more on this subject can do so at my writeup of Minnesota's Northwest Angle.