"eg" is fine without full stops, as are other common abbreviations, especially capitalised ones, at least here in the UK.

However, maybe now we could reintroduce the "e.g." form. I think open punctuation was introduced because when using monospaced fonts (eg on typewriters and golfball printers) all those extra punctuation marks look horrible, add lots of visual clutter, and increase the chances of rivers forming in your text. Now, 30 years on, we all use proportionally-spaced fonts and the punctuation marks don't look /quite/ as bad...

Hmm I'm not sure which is most important to me - pedantically following the rules of the English language, or clean, uncluttered typography... I enjoy both :)