Scott Bourne’s Photofocus blog reports that the ideal size for images on the new iPad is “2048-by-1536-pixel resolution at 264 pixels per inch (ppi)”. So that’s how you size wallpaper (or portfolio) images.
… and a Mashable article covers Twitter backgrounds, recommending dimensions of 1600px x 1200px. Another article by Christina Warren gives more detailed information on customising your twitter background.
AskeDee reports that Facebook cover images should be 851px x 315px.
Note: I’ll be editing this post as more common dimensions become available. If you’ve any you think should be added, please let me know through the comments.