What type of images are these? Are they like background, full-screen wallpaper, or images like photos to illustrate an article?
There are different ways to handle different types of images.
For background images, you can use media queries to display an image of an appropriate size for the screen.
For ordinary images, the sort you would put in the <img> tag, there are two new options, the srcset attribute and the <picture> element.
That’s fine for a photo, but displaying a 600px image larger than 600px will look bad, like in a full-screen image.
Using the above methods, you can have a number of versions of the same image at different sizes.
These are images in image tags, used to illustrate articles. In the past, I’ve generally used images no bigger than 600 pixels wide, using CSS to display them at smaller sizes in smaller screens. I just wondered if it would be a good idea to step it up to 800-1,000 pixels for people with bigger screens.
If the native image size is only 600px, I would not display it any bigger as the quality will degrade.
If you have a larger version which is 800px, that’s fine, but will be heavier for slower connections.
It depends on the site design. Many set a max-width on the main content container, so the image should look right in that size container.
Omitting a max-width can make the layout go a bit strange on big screens, as text lines get longer and the container height diminishes.
I should add that I was somewhat influenced by Wikipedia, which seems to prefer its images in the range of 1,000-10,000 pixels wide. But I’m increasingly coming to see WIkipedia as the exception that proves all the rules.