[alistairSH]

Not always. The boundary between VA and MD (states in the USA) is the Virginia shoreline of the Potomac River.

Which has caused oddities over the years…

At one time, gambling and liquor were illegal in VA, so casinos set up boats at the low tide line. Customers parked in VA and walked onto the casino barges from the Va side, but they were technically in MD.

You need to follow MD fishing regulations even from VA shore (though a VA license is ok).

[macintux]

My uncle once argued a case in the U.S. Supreme Court regarding Indiana & Kentucky's border, which was initially established in the middle of the river.

The Ohio River has gradually shifted south since the border was established, so some parts of Kentucky are now on the "wrong" side of the river.

[cozzyd]

The former capital of Illinois is on the wrong side of the Mississippi nowadays