Through most libraries, you can get ebook access to other library collections without having to wait for the book to come to you. If someone has digitized a book, chances are very high that you can access it through your library with the click of a mouse, or with the help of a librarian.
The Project Gutenberg website provides access to books that no longer fall under copyright. This is a boon for older books that are out of print. You can either download their books to keep, or read them on-site. Up to you.
Most of the library collections and Project Gutenberg use the ePub format. The app to read them is Adobe Digital Editions, and it's free.
With an Amazon Prime membership, you can "check out" up to ten books at a time through their Prime Reader program. It works just like a library: borrow book, return when done. Then there's Kindle Unlimited, which provides access to an even larger selection of books for a monthly fee. If you don't participate in either of those, Amazon has many free and inexpensive books available on a regular basis, and frequent sales on top of that, even of recent bestsellers. And even if they don't have the book for cheap, ebooks are almost always cheaper than print books. All of this makes Amazon definitely worth a look for the thrifty reader.
ETA: You need the free Kindle app to read Amazon ebooks "offline" on an iDevice or computer, but you can also read Amazon books with your web browser by going to any purchased or borrowed book's product page and clicking on the big green "READ NOW" icon.