Creative Commons has a “CC-0”, no-rights-reserved, search. Images that it serves up are free to use without restrictions.
WP Tavern offers a roundup of 13 sites. The first few paragraphs might get a little too deeply into the weeds for your purposes; the distinction has largely to do with if you’re sub-licensing a completed product such as a WordPress theme. Nevertheless, the images you’ll find here are licensed to about the freest extent possible.
Public Domain Archive has a selection of modern and vintage images, along with a weekly featured set. There are also some premiums items available. But the general set is free to download without registration. They don’t have a huge amount of inventory; any given category has from a dozen up to around 40 images, and many are duplicated across categories. But they’re easy enough to grab, and are large enough to use in any kind of banner or background.
Pickup Image appears to be a searchable compilation of a few thousand images and clip art from various contributors. All are large high-resolution photos free for any kind of use. I see a lot of landscape images. Registration is required to download full-size images.
New Old Stock is another compilation, this one of vintage photos from public archives. The home page shows a nice assortment of botanicals, historical landscapes and novelty shots in color, black-and-white, and aged-photo looks. No registration necessary, just open the image and save it.
The British Library is just that, the venerable institution’s archive of tens of thousands of images including antique maps, plans, diagrams, wallpaper designs, postcards, tracings of hieroglyphics, bookplates, crests, engravings — well you get the idea. They are grouped into albums or by photostream. There’s a search feature, but make sure you use the advanced section to have it search only tags; otherwise you get a lot of irrelevant returns.
PD Pics is another collection of all-purpose public-domain images. This would be a place to go if you wanted a generic image of car keys or a camera lens. Nothing artistic, just workable.
Gratisography is a sublime-to-ridiculous collection of very unusual photos. Playful, surreal, imaginative and workaday live peacefully side-by-side here. Most are beautifully done.
1 Million Free Pictures apparently has 1,000,000 free pictures. It seems that they’re all the work of one very busy photographer who has a few favorite subjects and a keen interest in Photoshop filters and effects. The resolution can be a little low, and they aren’t showstoppers. But they could serve a purpose.
Pixabay has a large selection of stock photos, vector graphics, illustrations and videos. These are the typical things you would see in any stock photo site — bright colors, interesting filters, multiple and/or time-lapse exposures. Pretty commercial and slick. Not that that’s a bad thing. They’re high-resolution and high-quality.
Unsplash is a collection of very beautiful contributed photos. Creative angles, clean color and composition, and a different point-of-view are the orders of the day.
Shutterography is a new service, similar to Shutterstock, which has a nice selection of creative images, offered for royalty-free, non-attribution commercial use.
I haven’t covered all the listings in the WP Tavern article, only because I didn’t like what they had, didn’t think it was appropriate, didn’t think there was enough and, in two cases, because the site was broken. Still, these will give you lots of good options. Enjoy!