What are the easiest to use sites for uploading screen shots and blend files so that I can share them with the community members?
SE automatically uploads images to http://stack.imgur.com.
For example, I uploaded the above picture by clicking the Image button and the picture was uploaded to http://i.stack.imgur.com/vQQKL.png.
As far as .blend files, you can use any upload site. I personally prefer Google drive for convenience, but other people use dropbox and other sites.
Edit (by GiantCowFilms)
We now have Blend-Exchange which is free and dedicated for hosting .blend files for this site.
It's exactly as Luke says, it's best to use the dedicated imgur site to upload images. Here is a post that can help you optimize the images that you upload. How can I optimize images and screenshots that I embed in my post?
As for blend files, you can use any service you like, dropbox, box, mediafire etc. The best one to use in my opinion however is PasteAll.org. The site naturally supports blend-files and even offers some security should you need to use it otherwise. The only con is that files are kept for ~5 months or so.
Here's my suggestion about where to post ~.blend files related to questions on Blender Stack Exchange: www.blendswap.dom, or another of the free repositories of ~.blend files in the community. Using of one (or more, if we want to avoid the appearance of partiality) of these sites would eliminate the issue of files being deleted, and would expose users, especially novice users) to valuable valuable Blender resource(s). It might be necessary to negotiate an arrangement with administrators and developers of sites used to permit deep linking to the blend file in a dedicated area on their site, to permit users who are not registered on the particular site on which a ~.blend file is listed to download the files in a question or an answer without the need for registration, and to allow the upload of files which might otherwise not meet site guidelines.
We might also want to add an icon to the editing icons directly above the edit box that would act on blend files the same way uploaded image files are added to the imgur site.