My quick-reference book on grammar suggests that the choice may also be (in fact, the author says it is primarily) geographic; i.e. that:
- in the UK (and potentially Canada), "Mr," "Mrs," "Dr," "eg," "ie," etc are not followed by a full-stop, and that
- in the U.S.A. (and potentially Canada), "Mr.", "Mrs.", "Dr.", "e.g.", "i.e." etc. are usually followed by a period.
N.B. the above handling of commas was also drawn from the same text (with a bit of tongue-in-cheek).
I have also often seen the periods exchanged for italicized formatting (for example: "eg" instead of "eg" or "e.g."); however, I have not see this convention addressed by a stylist "officially" (I also haven't really looked). That being said, if you find the periods annoying to type, I imagine you'd be even less enthusiastic about toggling italics on and off !
Personally, I try to prioritize clarity and consistency above everything else. This means that I make use of all three conventions, in different contexts; however, once I've chosen a convention for a particular context, I stick to it (this post being an exception; to my delight :D).
The whole thing has something of the same flavour as choosing how to pronounce words imported to English from foreign languages, when one knows how to pronounce the word in that language (e.g. "touché"). If my goal were to communicate clearly, I'd go with the option that I think would maximize the probability of doing so successfully (vs. if the goal were, e.g., to instruct).