Do you censor their library selections at all?
Yes. There are topics that are simply age inappropriate, and there are plenty of other books in the world to read instead. In addition, I steer DD away from books that I know will be "too scary" for her. She doesn't even like kid-oriented scary books (Goosebumps) and neither she nor I want to give her nightmares.
Do you encourage them to read books that might be more of a challenge?
Somestimes. This is usually unnecessary, because she'll pretty much read everything she gets her hands on. If I feel like she might need more challenge, I can just leave a challenging book laying around the house.
Somewhat related; do you struggle to find age-appropriate, engaging books that are 'safe' for very young readers?
Yes. It's tough. Talk to your local librarian, though, they usually have good ideas. There are also some threads on the Davidson forum with book suggestions.
Do you have a separate book allowance?
Yes and now. As far as a kid "allowance", no, because I am happy to encourage them without making them choose between a book and everything else in the world. We do have an "entertainment" budget for the whole family as a group.
Do you let them buy books?
Yes. For low budgets, I highly recommend checking out your local thrift stores. Some have better book selections that others, but kids books are almost always under a buck a piece, so you don't have to break the bank. You can often pick up some good magazines cheap at thrift stores, too, like National Geographic or Popular Science.
What do you do when you travel?
Well, when we traveled this summer we brought 1 carry-on size suitcase for me, 1 for the 2 kids, and 1 for the books. NOT KIDDING.
Which brings me to the question of eReaders ... do your kids have one?
Yes. We have 2 Nooks. I love them. We have 1 basic e-ink Nook. It was cheap, it's very sturdy, and a great reading experience for chapter books, which we can get at the library. And it's really really easy to increase the font size, which is important because my DD has terrible eyesight. Possibly from all the reading.
I also like the dictionary function, so she can look up the definition of words if she can't figure them out from context.
We also have 1 tablet-type Nook which is a better choice for books with pictures. I love it. It has a built-in profile system so I can assign particular books and apps to users individually. I only WISH I could get a kid-oriented user management system as nice on our actual computer.
On the subject of re-reading, I don't much re-read my books, but my kids both love to re-read books they enjoyed. DD in particular will re-read books that are challenging several times. This is a great strategy for improving her vocabulary and reading comprehension skills. DS, who is 4, enjoys re-reading for the story, but he's also more inclined to try reading words himself in books when we re-read them.