Like a prion, Alzheimer's protein seeds itself in the brain
sciencenews.org
sciencenews.org
In contrast neurons generally do not proliferate much after you're born (there's some debate about this, but even so a particular neutron is valuable because of the connections it has made, which are irreplaceable), so having each neutron kill itself when something goes bad would shortly leave you without a functioning nervous system. So neurons have to resort to more "creative" measures to clean up problems without destroying their entire cell bodies (e.g. autophagy, in which the cell cordons off a part of itself and then digests it). Naturally, these mechanisms are not as effective as demolishing the entire cell, so some problems can arise that neurons can't handle. But they are programmed not to kill themselves under almost any circumstances, so they continue limping along with only partial functionality or none at all.
Autophagy is a fairly recently-discovered mechanism (compared to, say, apoptosis), but it already seems to be a universally-used pathway, for everything from killing invading bacteria, to clearing plaques and aggregates of misfolded proteins (such as those that cause neurodegenerative diseases), to self-cannibalizing unnecessary cell components for energy and building blocks during starvation conditions.
There's some evidence that autophagy is protective against a wide range of neurodegenerative diseases, so a good bit of research is focused on how to stimulate autophagy in neurons in a safe and controlled fashion (since obviously too much autophagy will kill the cell outright).
What are the most interesting developments in research?
Here's a recent (published Jan 2012) paper claiming to show that exercise triggers autophagy in muscles, and that this autophagy is an important part of how excercise makes you healthier. http://www.nature.com/nature/journal/vaop/ncurrent/full/natu...
However, that paper says nothing about neurons, yet it seems to the basis of most of the "Could excercise stimulate neuroprotective autophagy?" speculation that I can find via Google. So I don't know that there's any published link between excercise and neuronal autophagy. I suspect that it's just the paper above showing a link between excercise and muscular autophagy, combined with the untested hypothesis of "Maybe excercise stimulates autophagy in other tisues too."
Neurons, in contrast, are special in that they are not replacable, since a "replacement" neuron would have no way of recreating all the synaptic connections made by the old one. A neuron's connections constitute information storage that would be irrevocably lost if that neuron were to die. Hence, neurons have evolved to spend lots and lots more energy keeping themselves alive compared to a typical cell in a multicellular organism, because the information stored in that neuron is (on average) very valuable to the organism. But life didn't evolve with neurons in mind, and it certainly didn't evolve with 100-year-old metabolically-active cells in mind, so this gets harder and harder as the cells get older, because they are pushing the limits of what cells are capable of.
As for Aβ possibly being the body's way of flagging problem areas, that seems unlikely, because such a function probably would not involve drastically changing its 3-D structure (i.e. going from "correctly folded" state to "misfolded" state), and certainly would not involve forming plaques. These and many other observed features are better explained as features of the pathology and not just a kind of damage signal reporting on the existence of a problem.
The prion-like behavior mentioned is the ability of prions to do something similar. Specifically, a small amount of abnormal prion protein can induce a larger amount to also become abnormal (with respect to it's shape). The process is analogous to crystallization, where small crystal can seed the creation of a larger one.
In the field, the significance of this is that small initial abnormal events can trigger larger ones within the brain, a bit like the famous butterfly analogy in chaos theory.