Here are my (last minute) thoughts on Alternative Vote versus First-Past-the-Post, as someone who's lived and voted under both systems -- I've lived in both the UK and Australia.
First, if I was in the UK I would vote YES in the referendum.
The reason is that AV lets me vote for who I want to win, without worrying about whether I think they can win. No more "Oh but in this constituency, its always been a two-horse race between X and Y so a voting for Z would be wasting your vote".
To knock out one myth, in theory it's not the extreme parties that benefit from AV -- it's the independents. Extreme parties (pretty much by definition) don't have broad support, so they don't pick up many second preferences. That should mean it's harder for an extreme candidate to get elected than a moderate candidate that everyone might put second. But under First-Past-the-Post, a moderate well-liked independent candidate faces a daunting task persuading voters that he stands any chance at all of winning against the major parties, so under first-past-the-post many people who might want to vote for him won't because they think their vote will be wasted. For me, that makes AV more democratic as the independent then stands or falls on the issues, not on gamesmanship about whether or not he can get enough other votes to be worth getting my vote too.
The side effect you do get in AV is the "How To Vote" card. In Australia, parties don't just care that you put them first, they also care about who you might list second, third, fourth, and so on. For example, Australian Labor (yes, it's spelt without the 'u') would much prefer you voted for the Greens second rather than the Nationals as a Green MP would be much more likely to support a Labor government in parliament. So each party has activists stand outside the polls giving you pamphlets telling you not just who they'd like you to put first, but the numbers all the way down the list. "How to Vote Labor", "How to Vote Liberal", "How to Vote Green", and other glossy pamphlets are thrust upon you on the way into to the polling station, in the hope of influencing your second and third preferences as well as your first. And the parties do some deals with each other (especially with the minor parties) around where they put each other on the "How to vote" cards
But the thing is, as a voter, I can completely ignore those "How To Vote" cards. So the side effect of AV is completely under control of the individual voter. But the side effect of first-past-the-post ("Will enough other people vote for this guy that he's even in the race? Am I wasting my vote here?") is bigger than any one voter and so there's nothing an individual voter can do about it.
In other words, you as an individual voter can stop the gamesmanship around AV, but you can't stop the gamesmanship around First-Past-the-Post. To me, that again makes AV more democratic.