Click on a social media site to see the maximum dimensions of key images for account settings, along with a link to official instructions. I’ll keep this list updated and let me know if you think something needs changing.
UPDATE: Here’s a quick guide from the Canva.com website, which is a handy, free online photo editor that I use for making images for social media (though you can use it for anything):
If you want an easy-to-use image resizing tool specifically for social media sites, give Social Image Resizer Tool a try. It automatically creates images to the spec listed above and includes favicons and app icons as well.
Update: Here’s a great infographic with visuals of all the social media image sizes going into 2016.