Libby - Ebooks, digital audiobooks, and magazines from your public library. Free, but requires a library card. Materials aren't infinite, so popular titles will often have a several week long waitlist. If you're in the US (or sufficiently crafty) you can sign up for a free card from the Queer Liberation Library.
Hoopla - Another service often bundled with a library card. The selection is smaller than Libby, but you have a limited number of instant borrows per month to cash in.
EBSCOhost Research - Ebooks and research materials, usually offered through a college. Where I do most of my reading lately, TBH.
Worldcat - Browse the world’s libraries from one search box. Easiest way to find out where to go to check out a book if you can't find it at your usual spot.
US residents will likely have a public library near them, but if you cannot go in person and sign up, there are a number of public libraries that don't require anything but a local address to get an Ecard. The libraries that offer this change frequently, so ask around.
Also keep in mind that US public libraries don't typically purchase self published material. If you're looking for your favorite tumblr author's book, you might want to try the links below instead.
Open Library - Large collection of ebooks. Some materials may not be available currently due to ongoing legal issues.
Project Gutenburg - Another huge collection of ebooks, probably the most well-known option on this list.
Standard Ebooks - Professionally formatted public domain ebooks (sourced from places like Project Gutenburg but then turned into dynamic epubs)
LibriVox - Public Domain Audiobooks. Extremely limited library, but provides a rare service.
Audible Free Trial - Amazon offers a free trial of their service, with one free title on signup. You need a viable payment method to get access, but you keep the book even after you cancel. Don't give Amazon your money, folks.
I'd also recommend trawling youtube and soundcloud for user-made audiobooks. The quality varies, but I've been surprised at the results.
StoryGraph - A non-Amazon GoodReads alternative, for those who like to challenge themselves to read more or enjoy writing book reviews.
Banned books list - Around since 1994 and currently still updated weekly, this site showcases books that are either banned or have been attempted to have been banned somewhere in the US. Some are available to read for free on site.