I wanted to call this post, "Great Books for Kids" or something like that. Until I remembered that what finally got Ironflower to read challenging (at the time) books independently was a series called, "
Rainbow Magic 
." The series probably isn't the most insipid and boring series ever written, but it must come close. However, it's about fairies and best friends, so it was like catnip to Ironflower. It helped that her actual best friends were into them too. After reading one aloud to her, I wanted to call up my former English teacher and apologize for everything I'd ever said about
Ethan Frome (for the record: I enjoyed Edith Wharton's other books a lot more). There are definitely books far more boring than Ethan Frome.
So I told Ironflower, who really had all her reading skills in place, that she had to read them for herself. Kid went from reading almost nothing by herself to reading several chapter books a week in the space of a month. So, yeah, that's why this post isn't about great books. It's about books that your kid will be so into that s/he will start reading for fun, or reading independently or whatever it is you're concerned about. Most of them are not (by a long stretch) great books, and that's okay. Let their high school English teachers worry about getting them to appreciate great literature, you just worry about getting them to appreciate reading.
Lovebug's "gateway" books were the
Captain Underpants series, with
Diary of a Wimpy Kid
coming in a close second. There's a lot you can complain about in Captain Underpants - the inappropriate potty humor, the disrespect for adults - but you can't argue with reading enthusiasm and vocabulary improvement. Dav Pilkey, author of the Captain Underpants series, also has a somewhat easier to read but still chapter book series called
Ricky Ricotta
. Ironflower is also a fan of the Wimpy Kid series, but what she loves the most right now is the
Dork Diaries
series. It's very similar to the Wimpy Kid series, but with a female protagonist. Another option is the
Babymouse 
series, which takes the tortured middle schooler theme and turns it into a graphic novel about a mouse.
Graphic novels are an excellent way to turn reluctant readers into avid readers. The pictures help with comprehension and lessen the anxiety kids might feel about reading "big kid" books. Lovebug enjoys the Daniel Boom series, where the kids all have a super-hero alter ego.
Some other graphic novels series that might appeal to your elementary schooler:
The
Magic Tree House
series has books that cover just about every topic, as well as male and female main characters. Kids who enjoy the adventurous spirit of those books might like the
Three Tales of My Father's Dragon
or the
Flat Stanley's Worldwide Adventures
series or the
Zack Files 
series.
If your kiddo doesn't like fiction, that's perfectly okay (until she has to pass an English literature class, anyway). For younger readers, there the
National Geographic Readers
series, with books on everything from
Planets
to
cats versus dogs
. Older kids can learn from the
National Geographic Kids Everything
series, which cover topics like weather and geology.
Landmark Books
publishes books that cover famous people throughout history, like Abraham Lincoln and Ben Franklin. And while not exactly non-fiction, the
I Survived 
series gives wonderfully accurate accounts of what happened during various historical occasions throughout history.
And don't rule out picture books.
Patricia Polacco, for example,

writes compelling picture books that introduce lots of challenging vocabulary words and talk about different cultures. Comics like Adventure Time, and magazines like American Girl and National Geographic Kids are not books (obviously) but if your kid enjoys them? They'll totally work.