And there are remnants of French Canada
Marble Hill is a section of Manhattan on the mainland.
Another one: Jungholz, Austria, an enclave within Germany that connects to the rest of Austria at single point. That point is at the summit of a mountain, although not an especially tall one. You can hike to the top.
Yes that’s the general principal recognized by most countries without need for a specific treaty for each place, that countries aren’t allowed to prevent maritime transit through their territorial waters for ships going elsewhere. In any case it’s the principal accepted by the countries surrounding the Kaliningrad Oblast and since the countries in question also accept the international standard of 12 nautical mile territorial waters (as opposed to 200 nm Exclusive Economic Zones for stuff like fishing and oil rights, environmental regulation etc) ships do not have to enter non-Russian territorial waters between Gulf of Finland ports in Russia and the KO. Though they might do so to minimize distance when rounding the Estonian and Latvian coasts.
The KO is mainly remarkable because it was the western end of contiguous Soviet land territory not that long ago, and was annexed after WWII with no intention or expectation of it being otherwise.
South of “the City and County of San Francisco” is San Mateo County which contains San Francisco International Airport on unincorporated county land owned by San Francisco. I’m not sure if that’s an exclave.
There are also a number of Spanish enclaves in Morocco. The best known are Ceuta (that was my first trip to Spain!) and Melilla, but there are also the Plazas de soberanía.
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And don’t forget Kentucky bend, a bit of Kentucky that cannot be reached by land, air, or water without going through either MO or TN. It is completely surrounded by those two states.
You know, while this topic has come up many times before and listings of such oddities get posted in those threads, I still enjoy the fact that there are people like the OP who have freshly discovered a concept such as this and is happy to ask more about it.
Finding out about stuff is good.
Similarly, Carter Lake Iowa is the only part of Iowa west of the Missouri River. It is almost entirely surrounded by the city of Omaha.
Fishers Island, NY can’t be reached by a land vehicle without going through Connecticut. It was part of my home town, but takes 3+ hours to reach because you need to take two ferries.
New jersey and Delaware are separated by a river and bay…except for a tiny sliver of land on western Jersey belonging to Delaware.
Carter Lake is among my list of noted fun oddities, but you can get to it from the rest of Iowa by air or river. Still nifty tho.
I think that Kentucky Bend and Liberty Island are the only true state exclaves in the US. Tho I’d love to be proved wrong.
Technically, crossing by boat from WA to Point Roberts takes you out of WA and into Federal waters, so some folks argue it’s a true state exclave also. I’m undecided. 
Also, how many know that NY state and Rhode Island share a border? Just past Fisher’s island, you can sail or fly from NY state directly into RI . . .
And I love that Illinois’ early capital, Kaskaskia, is WEST of the Mississippi river.
The story of that is that for some reason I have not been able to discover, the boundary between NJ and DE was set at the NJ shore rather than the river channel, as usually happens. Then some landfill was dumped by the shore and created new land, which then belonged to DE. No one lives there and I doubt that DE actually does anything with it.
I believe that Kaliningrad (not Kalingrad) was a Russian naval base and actually part of the Russian SSR and kept when the SU disappeared. It was formally Koenigsberg, made famous by the 7 bridges that Euler studied and thereby invented graph theory.
I’m a bit surprised that no one has mentioned the Delmarva peninsula. Although you can cross Chesapeake Bay from VA or MD to their respective territories, you can get to them by land only by going through DE.
Besides Kaliningrad, Russia acquired another exclave when it annexed the Crimea from Ukraine, although this is not widely recognized.
If you hang a right onto MD 213 at Elkton, you can drive down the Maryland Eastern Shore w/o entering Delaware, crossing over the C&D canal by bridge at Chesapeake City.
There’s this strange enclave-in-an-enclave that exists within Oman and the United Arab Emirates.
Although recently the first train arrived over a new bridge from Crimea to Russia, so technically not an (illegitimate) exclave any more.
Apparently there are plenty of places along the Mississippi that are on the “wrong” side of the river, thanks to its propensity to wander since boundaries were drawn.
As of 1998, there’s also Ellis Island. Its original boundaries and a small bit of reclaimed land are part of New York, but the vast majority of the new land is now legally part of New Jersey. (It’s about 3.3 acres NY, 24.2 acres NJ.) The New York section is completely surrounded by New Jersey land.