The abbreviation etc. requires one period at the end. The abbreviation e.g. requires two periods, one after each letter. This has not changed to the best of my knowledge, and so I personally would consider writing them otherwise as incorrect, or at best nonstandard.
The abbreviation Mr. traditionally required a period, but it is becoming increasingly common, even in the most respected publications, to see it printed sans period.
When in doubt, check the style manual of your choice. Mine is The Chicago Manual of Style.