For this, (as the question, that the link links to, has been removed, "this" refers to sharing a banner on 3rd party websites concerned about limited resources) I'm looking for a free and reliable host for images, where I can share the image with a direct link. Google Picasa is not a good option because it produces a very long direct link, any other suggestions?
Are you just trying to share a banner image? and have it hosted/served from somewhere? You can use windows skydrive, google drive, or dropbox.
You can also put it up on a cheap godaddy instance or amazon aws and setup cname in dns settings so you can have an easy url to point to the image file.
If you'd like to share images with people via a download link, Dropbox.com would work for you. You'll be limited to 2 Gigs free, but if you just have projects to share from time to time, dropbox lets you send people a link where they can view/download the pictures.