I've been reading Chernev's 1000 Best Short Games of Chess with the intent to memorize each game (harder when the text is in descriptive), and then entering the games in a database from memory. Packing a game into short-term memory is not too difficult; getting the good ones into long-term memory might require a physical chess board and pieces.
How many books to read before you're a master?

I think it is part of learning to actually touch and move the pieces (tactile memory), plus, as Master de la Maza pointed out this is a good way to get board vision and board awareness.

e4nf3 heads to the loo (sorry, from some reason I still seem to think of you in Greenland--maybe because I've never before known anybody from Greenland)...

You can also look at it in a zen-like light; you can never arrive to be a master, but travel along a never ending journey.

Humans are too complex to make any firm generalizations. Kid prodigies throw a wrench in a good # of theories I'd think. What a waste of time looking for a trick or simple equation

The problem with Books is that there are more of them than GM players. Books are great for getting you to think, but they can't do the thinking for you and at the end of the day, its just you at the table.

I've got somewhere between 20-25 chess books I think, though I have put some aside because they are beyond my current rating level. It's not that I can't read them and understand/gain something from them (My System, Art of Attack in Chess, FCO) it's just not worth my time investing in these much yet, when tactically I am still a little blunder-some at 1400-1500.
I've got a degree in Literature so naturally when coming to study chess this year I turned to books first and foremost as a learning method. I still go through strategy based books everyday - right now I'm going through Stean's Simple Chess and Logical Chess by Chernev and trying to stick to those two (though I have another one in the post and I can't even remember what it is). I'm thinking better to read two in depth over twenty sporadically. It is a pain though because nearly ever time I come on the forum I end up ordering another book, so I must be disciplined.
I know that the best form of study for me though is tactics and analysing my mistakes with the help of a stronger player. I really need to join a club next though I think and play longer games. I play standard 15/10 on here but the standard 1 hour for the first 30 moves in club chess I think would be beneficial for me.
I would be very surprised if someone could make master level without reading books. I suppose it could be done and maybe has been, but it seems silly cutting off study from books - a major source of knowledge - and just playing. Balance is probably the key.
Yes, you always have to make the move on your small chess set.