Do you mean what our children are reading, themselves, silently, all the way through? Or could it include books they pick up and flip through at random and then carry to another part of the house and drop? Might it also include books we read to our children? These would be three very different lists...
My older (now about 4.5 years) doesn't seem to read many books cover to cover by himself. He does this with some Berenstain Bears books, and occasionally some harder books, e.g., re-reading some Usborne books I've read to him, but more often really easy baby books, just for fun.
He carries around with him and flips through
all sorts of books, but I couldn't really say how much of these he reads. Sometimes he reads a lot of them, but more often he's obviously just skimming, or even just toting a much-loved book around like a teddy bear.
As to the books I read to him, well, we've done a lot, there's no way to make a short list even of the books we've read lately. Bedtime reading has included easy versions of
The Time Machine, which he loved, and easy versions of
Peter Pan, The Invisible Man, The Call of the Wild, and quite a few others. We have really gotten into the Usborne Reading Program books (
http://www.usborne.com/catalogue/usborne-reading-programme.aspx?area=YR) and the Great Illustrated Classics series, which is really great--excellent transitions from picture books to chapter books, as they have a full-page picture on every other page. As to original books for bedtime reading, we've gone through the first (long) chapter of
The Jungle Book recently, after reading no fewer than two easier versions previously. We also
listened to the whole thing (the original) in the car. Let's see, then we also almost finished the first Encyclopedia Brown (he said he wanted to be as smart as Encyclopedia Brown!), read the whole Usborne Illustrated Classics for Boys which has a lot of great stuff, etc. That's just the bedtime reading. Oh, and recently, we started reading this Paragon one-volume Q-and-A encyclopedia about the U.S.A.--I have my regrets about this because it is so badly edited, I caught several mistakes just in the first chapter. He's pretty interested in it maybe because I supplement it with pictures found online of the different things discussed (I have the iPad next to the bed lately).
At mealtimes we still read a large variety of books, mostly nonfiction. Not infrequently I arrive at the table ready to read something and he's already reading something himself, so I just pick up the newspaper. (Obviously, in our family, reading at the table is not regarded as rude.) To be honest, sometimes we don't do anything very educational at mealtime, but we're keeping up with it more or less. A harder book that we recently finished at the table was D-Day Landings (DK Readers). This has an interesting personal story to go with it. At some point a few months ago, somehow D-Day was mentioned (possibly it was in some book, but I forget), and I told my boy the story of D-Day. He was greatly impressed, and then that evening he said he was going to tell me a story, and he proceeded to tell me the D-Day story in great detail. Then he demanded to get books about D-Day. I finally got one (it was hard to find one that was even possibly accessible) after a few weeks and he wasn't interested then. But he did finally get it out and ask to read it, so we did. Pretty dry stuff, for a lot of people, I imagine, but I did my best to keep it exciting, to explain everything possibly puzzling (he stares at me expectantly whenever he doesn't understand something), getting out a map or globe or the iPad for extra illustrations, etc.
I was also surprised when he was willing to go all the way through the Usborne
Alexander the Great book. He was talking about Alexander for the next few days. Now we're halfway through
Julius Caesar. He's really learning history now (we also read the Usborne book about Rome, and others I'm sure), I'm very pleased to say, and I'm kind of surprised as well--all of a sudden, he's interested in it. And not so crazy about transportation...
We read lots of "leveled readers" many of which are about different animal groups and topics in science. We have read many, many of the "Let's Read and Find Out" science books, there's a huge number of those ones and they're all great!
But...I think you mean books that your child reads himself. I wish mine would read in a more disciplined way, but I am not going to get too worried about it, he's only 4 and he does read some to himself...