In reply to Phil Scott:
I have the OEAV (AAC) membership (in addition to my club membership, since I want to support their work locally), and with the alpine huts discount (and reciprocity with the French and Swiss and other clubs), in my case it usually pays for itself. As the discount is usually around 30-50%, paying 13€ instead of 25€ for one night at a hut adds up quickly (although some alpine huts are privately - not club - owned, without any discount). It highly depends on where you go and how many nights you stay there, so do the maths yourself.
The rescue costs coverage (I think around 25 000€, a must, as in most Alpine countries, mountain rescue services are paid, and a heli flight is costly) and Europe-wide third party liability coverage (again a must, I think 3 000 000€, as with third party injury the damages can be very high) is a welcome bonus that I have had the fortune of not needing yet
Although, as others noted, the insurance is mostly rescue, repatriation and liability coverage. The health insurance is very basic (10 000€), since most of the OEAV members have their own EHIC national coverage. And even with the EHIC or equivalent, you could possibly (?) exceed that if you had to be flown to a private hospital with the public one out of reach due to weather conditions (while they would probably transfer you to a public one via ambulance asap, you might not want a transfer while severely injured).
Better to get a separate travel health insurance as well (which might negate the savings on the huts, since some travel insurances have good mountaineering rescue and liability coverage anyway). It really pays to read the fine print and do the maths. There are many options and combinations. Even some other alpine clubs with favourable insurance coverage (although navigating them as a foreigner could be quite difficult).
Post edited at 15:15