My daughter is 15, and I only have her a couple months a year. Still I've been able to turn her into a voracious reader. Not just for recreaction, but academically as well. While the rest of her class is reading wiki's and middle school books on historic figures for their reports, she's tackling peer-reviewed journals and college level biographies (even going so far as to look into the bibliography and get primary sources). Books are generally the only (or one of a couple) things on her wish lists and present lists.
If I had to assess why I'd say it has three sources:
1) I read to her ALL the time growing up
2) I, and those I associate with, supply constant positive reinforcement for reading
3) I do my best not to ever provide her answers, only guide her to finding them herself (which requires reading)
I don't severely limit digital entertainment (though we don't focus much on tv here), and in fact she's quite the budding gamer chick. It hasn't seemed to diminish her love for, or ability in, reading.