Should the periods be omitted in e.g. and i.e.? Is it totally incorrect to do so?

John wanted more to life, ie, he wanted a wife and kids.

Bring to the picnic what most people snack on, eg, apples, oranges, and pretzels.

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Comments  (Page 2) 
I was told in typing class that it was going out of style to use periods in abbreviations such as am, pm, ie, eg - due to the 'look'. It was apparently too busy and probably slightly annoying for typists to punctuate. I'm not sure if this was true at the time (this was a decade or so ago). Perhaps with the rise of modern keyboards and typography, punctuating abbreviations isn't as clunky or aesthetically displeasing. Or perhaps, my typing teacher wasn't properly informed or I may have misunderstood. In any case, I have not used periods since although I will from now on (after this post).