What is the conventional way this is handled: geographical boundaries that are set by a river that changes its banks over time. For example, the Mississippi River in the U.S. defines part of the borders of several U.S. states and is notorious for changing over time. I saw one documentary that compared how the Mississippi River looked every ten years and there were significant changes all the time.

I would assume that in the case of state boundaries within the U.S. the answer would that the boundary is, quite simply, the river (as it is at the relevant time). I suspect that the position would be the same for international borders.

The Rio Grande river is the international boundary between the U.S. and Mexico (for our friends who aren't sure).
It's been twenty-something years since the river changed it's course and left a small island in the middle.
Some enterprising adventurer claimed the island and tried to establish a new country. He wanted to issue passports, coin money, establish diplomatic relations, etc.
I don't remember the outcome. He was probably ignored by both countries until the Rio Grande flooded again and wiped out his new nation.

There's an area of Iowa on the west side of the Missouri River WITHIN Omaha, NE, called Carter Lake. I'm told the reason for this little off-shoot of Iowa is the altering of the river which serves as boundary and the desire of Iowa to keep the lake after the river changed course. I'm not 100% certain. But I do know that Nebraska sued Iowa for rights to the property after the course change and lost in a verdict handed down by the US Supreme Court.

Lothruin, the example you cite is very interesting and may answer my question. Can you point me to this court decision?

In Canada (Saskatchewan in particular) properties that are bordered by a waterway or lake are usually defined by the high water mark as originally surveyed. Waterways and lakes are held in the right of the government therefore even a dried lake is still a lake. A moving geographic feature that serves as a border is an interesting problem but should all be dealt with through previously negotitated treaties which may be different in each circumstance. My guess is that international boundaries would maintain access to the waterway but local boundaries would maintain specific geographic area.

http://www.justia.us/us/406/117/

There ya go, root.

Basically, I think what happened was that previously the area where Carter Lake is located was to the East of the line of the Missouri River, but the course of the river was deliberately changed sometime shortly before the turn of the century, for reasons not pertaining to the appropriation of property. (In other words, someone changed the river, and given the nature of the river, it would have had to be Iowa and Nebraska working together, and the purpose of the change was NOT to afford one state the property around Carter Lake, but some other reason.) However, after the river's course was changed, Nebraska sued Iowa for the Carter Lake property, now on the West (Nebraska) side of the river. Nebraska lost. The court ruling you see above was from the mid 1970's, when Nebraska AGAIN sued Iowa for the Carter Lake property. It seems that the US Supreme Court decided that for all future dealings, the center line of the river itself was the boundary, and natural shifts of the river WILL change the property, but Carter Lake is an exception becuase the river was changed deliberately, and so the Carter Lake area remains a part of Iowa unless the river ever shifts from the easterly (man-made) course, back to the original bed, so that it is West of Carter Lake, and then naturally shifts BACK to the East side. If that ever happens, Carter Lake will become a part of Nebraska through the natural shifts of the river, but it is unlikely such a thing will ever occur, and probably wouldn't be allowed to occur anyway, since it would have to wash out developed property in order to do so.

How this pertains to other rivers I'm not really sure, but part of the suit Nebraska filed included establishing a set boundary. The US Supreme Court did not do so. The boundary between Iowa and Nebraska is a "varying boundary" set by the centerline of the Missouri River bed. This has always been the case, and the Supreme Court simply upheld the precedent. I would imagine that in other cases where a river is the boundary, the same applies, or the Supreme Court would most likely have agreed to Nebraska's request to set a fixed boundary. However, there may be other parts of other states where the Supreme Court has done what they did in the above case, that being that while the majority of the state boundary is a varying boundary, certain portions of riverside properties are set with fixed boundaries.

In most countries rivers have been an easy way to define local and national boundaries, and of course in England we manage to make some strange exceptions as well, the reasons for which remain a mystery to me.

In my local area the River Thames forms the boundary between the old county of Middlesex (and still does postally), and Surrey, but for a reason I don't know, an old map shows the boundary crept across the river at Laleham as it still does postally as you can see here, and Surrey also creeps into Middlesex at Chertsey lock. Another old map appears to show Buckinghamshire crossing the river into what would otherwise be Surrey at Wraysbury as it still does now as well. Having seen your theory though it may well be following an earlier course of the river as of course they do change over time, so that may well be the reason.

My nearest river is the tiny and often stagnant River Brent, which also became the new name for the borough when Greater London was created in 1965 and Middlesex was absorbed. But though the river crosses the whole of North-West London, the small suburb actually named Brent, in the north of Golders Green was in the new borough of Barnet as the borough was named after the river itself rather than the small area that also had the name.

Other conflicts have made towns into using postal counties they aren't even in, one I discovered being the village of Marsworth, which is in Buckinghamshire, unless you're posting a letter there in which case it miraculously moves to Hertfordshire. Of course it has never really been anywhere except Bucks., but sadly the postal service has used postal delivery routes to redefine its personal boundaries, which only bear a passing relation to the true ones, so we have always had two sets of boundaries, those dictated by maps and the alternative we have to write on our addresses. Nowadays our counties appear to change every few years but few places are in different ones at the same time as Marsworth besides in Greater London, which kept the status quo postally when it was formed by absorbing parts (or all) of neighbouring counties. Previously there had been a county of London, but even that was a Victorian invention when London, originally a town in the county of Middlesex, spread so far across the various neighbouring counties it occupied by then. The other counties (until rearranged in 1975 and ever since) were more or less the same from their original formation so London is exceptional. And no, we still find it just as confusing even though we live with it. Another reason the French probably laugh at us as well...

Until well into the Victorian period (the 1880s, I think) the English counties were riddled with exclaves, enclaves and sundry anomalies.

I have heard it said that when England was first divided into counties, if a manor crossed a river or other nominal county boundary, the individual manors were as far as possible kept in the same county, so one didn't have different (bye-)laws in force on different part of an estate.

Lothruin, thanks very much for pointing me to this link. That was a very interesting court case.