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This is only a problem if you take an absolutist line, which I don't think anyone really does. Even the toughest libertarians still want a police force and law courts.

That is in fact the key difference between libertarian and anarchist.

If a philosophy doesn't work in absolutist terms, perhaps it shouldn't be expressed in absolutist terms. The parent comment left no apparent wiggle room.

Meh, people are lazy with language like this all the time. Many people say "murder is always wrong", but, when you ask them, say "well, self defense is ok". Instead of assuming the worst possible case for your opponent, be charitable with his case. You'll avoid nonsense discussions much more often.

- I own a square mile of land with a river running through it. You own an adjacent square mile of land downriver of mine. If I, entirely on my own property, divert the river such that it ceases to run through your property, have I aggressed against you? Do you have the right to never have the value of your property decrease?

If you change the flow of the river on your property such that it affects mine, then yes you have aggressed against me (it is easier to see in the reverse, it is clearly an aggression against me if you flood my land even if you poor the water on your own land).

  - I am fantabulously wealthy and buy up all the food in
    the world.  Do I have the right to refuse to sell it?
    Have I aggressed against the other 7 billion by forcing
    the large majority of them to starve to death?

You have the right not to sell it, and no you haven't aggressed against anyone assuming that the food had been payed for (whomever sold you the food must have valued whatever you gave them in return more than the food)

  - The local branch of the Nazis are hunting for members
    of unpopular minorities.  I am a gay black Jew.  Am I
    justified in trespassing on a stranger's property in
    order to hide and evade capture?

Strictly speaking no you don't have to right to hide on their property (and if the Nazies kill those suspected of hiding minorities they are in danger too) though I doubt anybody would have a much of an issue with it if you did.

"If you change the flow of the river on your property such that it affects mine, then yes you have aggressed against me (it is easier to see in the reverse, it is clearly an aggression against me if you flood my land even if you poor the water on your own land)."

Once you accept this, things start getting very complicated. For example, if your factory spews carcinogens into air I breath, it follows that your factor is an act of aggression a la the flooding of the river. Now substitute carcinogens with any pollutant, (perhaps even noise pollution, or visual pollution (eg. I had a nice view before you built that ugly building there) ) and it can quickly get out of hand. The line must be drawn somewhere, and the place that the somewhere is drawn is kind of arbitrary. Very intelligent people can disagree whether or not the line ought to include greenhouse gases.

Btw. I fully agree with the river example.

I completely disagree with your second example though. Off in the real world, its very easy to leverage your wealth to extract unfair agreements from people. The 'all the food in the whole world example is silly', but history is full of examples of people hoarding commodities that are necessary for survival and then exploiting that hoard for ridiculous enrichment. I think at some point, people a right to do something about those sorts of hoarders.

Voting cannot be considered a negative right. I have no more of a negative right to tell the individuals in my government what to do than they have to tell me what to do. I do have the negative right to give them the privilege of governing me and my property just the same as they have the negative right to protect me and my property and to give me the privilege of having some say in their decisions. If we come to that agreement, then I have the privilege of voting and they have the privilege of governing me.