When I think of double negatives I think of phrases that grate on the ears, like:
I'm not going to do no homework.
I'm never going to not go visit Graceland.
There are some phrases that appear to technically be considered a double negative, but seem more common and are, in my opinion, actually pleasing to the ear. And I've seen such uses in newspaper articles, magazine articles, and other edited content.
I'm referring to phrases like:
It's not uncommon for two people to meet serendipitously.
Baseball is not unlike golf – both are boring to watch without a beer in hand.
It's not unusual to be loved by anyone.
Are the above examples of double negatives? Should their use be avoided?
Best Answer
To answer your first explicit question, I would say they are double negatives:
To answer the second question, I would say the use of litotes is perfectly acceptable.
The respective Wikipedia articles (linked to and excerpted above) give a lot of good information. I would like to emphasize the potential ambiguity in litotes, in that the intensity of the double-negative-as-positive ranges from "mildly positive" to "resoundingly positive".
Finally, see this other EL&U question covering the specific example of not uncommon.