It's really all up to what you are after and what your viewing "media" will be, as well as what the viewers are using to view it!
My Web host PBase uses 800 pix as the "standard" large viewing size, so an image that I upload will be resized to say 800x600 pixels, but I personally find that small for what you could call "gallery viewing", so I upload to a larger size and then use the PBase "Original" size for image viewing.
And then, we have POTN here, which has been using a "standard" viewing size, max of 1024 pixels at the widest. It's a bit out-dated for our modern systems, and is in the process of being upgraded, but still since POTN has been my main place for "image sharing" when I upload pics to PBase I typically have them at the 1024-pixel standard for the "original" viewing size.
More recently, though, I've been checking the other options out there. For example, I'm not a Flickr user and don't have expertise, but I know that there are a couple levels. The free Flickr account lets you upload photos and then resizes them to the "standard" viewing sizes. The "Pro" (for pay) account, though, lets viewer see the photos in the "original" size so, like my PBase (for pay) account you can view those photos large!
Well, that's well and good, except that the photos may in fact be too large for my viewing screen!
Well, not long ago FaceBook came out with a cool option -- you can upload a large-res photo and viewers can choose to view in the "Full Screen View" mode. What this does is when it loads a photo in that mode, all extra "stuff" goes away and you get a nice view of the photo with black frames. And then, if the photo has a nice large resolution, FaceBook will render it to fill your screen. But if the image is too high a resolution for your viewer, it will back off -- fill your screen with the whole image, not overflow. Smaller-res images will just view at their full res.
I know that FaceBook has had a bad rep with a lot of folks for how they handle images, but since I've been playing with this I upload images at a "medium" resolution, which for me is about 1600x1000 pixels, and I've been quite happy. And, since I interact with a fair number of photographers on FaceBook, a lot of them have taken to my practice of uploading nice large images and then informing people to make sure and view them at the "Full Screen View" mode to get the most out of them!
I'm not sure of the specifics, but I believe the new version of POTN when it's released will have some viewing flexibility...it will have a "max" resolution but larger than the present 1024 pixels, which is to me a good thing for image sharing!