I think it's clear that e.g. has to have full stops/periods. It is an abbreviation for exempli gratia and is technically an acronym, in which each of the first two letters is used. These are always presented either with full stops, capital letters or both. Thus, we do use US and could use u.s. if it was not a country name, but could not just write "us." As for putting one full stop at the end that is for abbreviations where the word is "cut," not acronyms so we use abbr. for abbreviation sand adj. for adjective, but could not use eg., unless the word was "egsample" (har har). As for using a comma after it, that should only be done in some cases, like my last sentence (see what I did?). At the beginning of a list, it is wrong. Why not follow logic rather than convention, or if you follow convention, follow all major style guides, which use e.g. I recently wrote a blog post on this issue at http://www.makeyourenglishwork.com/2012/05/17/eg-or-e-g/ if you're interested.