There are lots of options for sharing images online, but Snag.gy is about as simple as it gets. Paste the contents of your clipboard onto the site, using the oh-so-familiar Control-V shortcut, and it is immediately uploaded. You can crop and perform simple edits, and the image is immediately available for sharing.
There's really not much more to it than that, though there is an option to delete images and also a surprisingly extensive list of keyboard shortcuts. As well as pasting actual images, you can also paste URL links and file paths. Simple and effective. Thanks Thomas for the tip!