There are tons of books lists out there. Seriously, search for "best books for ESL" or "best books for English learners" and there'll be millions of search results. So, here are my disclaimers. This list is, in no way, a definitive list of English classic books. There are other pages for that kind of thing. It's not a list of the absolute best books for students of English (because that's a list that doesn't actually exist anywhere, since book preferences are subjective).
However, this is a list of some good, classic, English books that provide a place to start if you're having trouble finding something to read! Here are my basic criteria that I used to choose the books for this list.
1) Length. Basically, I recommend shorter books for lower levels.
2) Availability. I like free books! And (free) books online are excellent for people who may not have access to a large selection of printed English books.
3) Classics. I went with a very loose definition of 'classic'; generally, I chose books that are either widely read, or at least widely known through some other medium (such as movies).
A Collection of Beatrix Potter Stories by Beatrix Potter
Mr. Bean in Town by Richard Curtis
Aladdin by Ruth Hobart
Alice's Adventures in Wonderland by Lewis Carroll
The Gift of the Magi by O. Henry
Charlie and the Chocolate Factory by Roald Dahl (http://www.readanybook.com/online/127)
Anne of Green Gables by L.M. Montgomery
David Copperfield by Charles Dickens
Cat Among the Pigeons by Agatha Christie
Emma by Jane Austen
Upper Intermediate/ Advanced
1984 by George Orwell
Hamlet by Shakespeare
Time Machine by H.G. Wells
The Three Musketeers by Alexandre Dumas
In the end, the best English book to read is the one that you want to read! Do you love a book that's been translated from English? Find that book in English and give it go. A good rule of thumb to follow to determine if a book is too hard for you is this: if you don't understand the gist of the first few pages, it's too advanced, so put it aside and try another one.
Unless otherwise noted, all books can be found at one of these library websites.