Well, as you might be able to tell from my tags, I love the game.
I started off running 2nd ed and have played in and/or run every edition since, including doing quite a bit of playtesting for various supplements and the core book for the current (5th) edition.
What do I like about it? Well, the setting for one, as I am a bit of a medieval history nut, but much more importantly I like the communal feeling of the game. In a large sense, you are not creating a character, but a whole village, in that everyone creates multiple characters and there is a tendency (seen over multiple sagas) to keep creating the background characters for your covenant (various servants, farmers, etc. -- almost 100% noncombatants, but still interesting to know about).
I also love the sense of the passage of time. In most games, time is primarily important in the sense of how many rounds of combat have passed, but in AM there is actually the feeling of time passing in terms of seasons and, of course, years. I still remember the reaction my group at the time had when a grog (warrior) died of old age (rather than combat or disease) -- it was a sobering experience for the group.
The magic system is what first drew me to the game. The sheer level of flexibility in it is something that always makes me happy. I have seen players go utterly combative in their magics, utterly noncombative, and all sorts of washes in between. To be fair, though, many people find the combat system somewhat less exciting, but that is not the real focus of the game, so it makes a certain amount of sense (the sheer fact that each edition has radically rewritten the combat rules may give you a sense of what they got right -- magic, Virtues & Flaws -- and what they were less satisfied with).
AM is, however, a difficult game to get people interested in, at least compared to D&D. In rpgs, D&D is the tail that wags the dog -- it is everywhere and well known, thus it is much easier to get people to try. AM tends to draw on older gamers who have already tried other systems and found them missing something in one area or another, but it has never been a major system or one that is easy to find. It is, in many ways, a specialty game, but it is one that I adore.
I will gleefully answer any PMs on the topic.