1000x1000 pixels should be about max.
Not everyone is good with photos though, some are just starting out. Photo editing programs have a resizing function though and popular photo hosting sites have editing options if one doesn't own their own.
800x600 is a fairly universal standard for large images on discussion forums (and 800 is TFL's maximum for uploads). Anything larger than that is fairly obnoxious, unless the additional size is being used to show extreme detail. (Even then, 1024 pixels should be the maximum width used, and cropping to 800 is still preferred.)
For most purposes on TFL, a width of 600 or 640 pixels is more than enough.
Coincidentally, widths of 480, 600, 640, and 800 pixels are usually standard options on image hosting sites. They make it easy to just copy the link corresponding to the size wanted.
Just keep in mind that even if you run high resolution on your own monitor, other people may not. Some people, like me, might be running at resolution like 2560x1440 or 2560x1600; but it's still more common for people to be running 1280x720, 1024x768, or even 800x600. With the lower resolution, large pictures can't even be viewed in their entirety without scrolling around in the browser window.