I wish there were a simple one size fits all answer to the best exposure compensation (EC) settings.
For me, exposure compensation is perhaps most useful in situations where one is taking a series of shots under similar lighting conditions. Based on histogram results from the first photo, one can dial in a compensation that will ensure that the rest of the photos turn out just right. This is particularly useful for certain indoor events where you want to set a mood, and/or where there is an overabundance of light/dark (such as a tuxedo shoot at a wedding with the grooms, or bride's maid shoot which frequently has a lot of white dresses). Other situations include photos at a white sand beach, in the snow, near dark rocks, etc.
Perhaps what you were hoping for here is how to use exposure compensation *in anticipation* of your first photo. The simple answer here is that if you can, always take a test shot first. For those situations where this is not possible, the best EC setting unfortunately really just comes from experience. Many types of scenes have their own rule of thumb, and photographers accumulate these over the years in their mental catalog of settings. There are a few clear-cut examples though, with snow photos or shots at the beach being perhaps the most common.
examples of situations which required positive exposure compensation
Even before my first snow shot, for example, I dial in at least +2/3 EC because I know the camera's metering system will grossly underexpose-- I just don't quite know by how much. I of course later may need to increase this EC amount, but at least it prevents the first photo from being unrecoverable. Again, I think this is the key:
take a quick test shot under the same lighting/composition to get an accurate estimate of the amount of exposure compensation that is needed. This will work in 95% of situations, and will really improve similar subsequent photos.
Another time I have found EC useful is when I want to err on the side of caution with my exposure. If I am shooting in RAW mode, sometimes it's OK to underexpose a little if it assures me that none of my shots will have any blown highlights. Situations with fast-changing and unpredictable light are best-suited for this precautionary EC technique.
situation with fast-changing, unpredictable light where negative exposure compensation was helpful
There's a little more on this EC topic on this site's tutorial about
camera metering & exposure, with exposure compensation specifically addressed some at the end...