Here's a picture of the Masonic ring I now wear. I wear it proudly and am glad to answer questions about the ring I get from co-workers and the like. I was fortunate enough to plan ahead and wear it the day of my raising (afterwards, of course).
In my preparation, I noticed the other brothers' rings and asked where they go theirs, etc., and one thing I noticed was that all of them had their rings with the points of the compass turned in (that is to say that if holding their arm out straight, the G would be facing them). The common school of thought is to wear it inwardly focused as a reminder to improve themselves. To continue on with this thought is that after one has become a Past Master of a lodge, then they can point the compass outward as a symbol of accomplishment.
I have decided to take another approach. I wear mine with the points outward, for others to see. I do this not in arrogance, but as a reminder to myself that I am "broadcasting" an image of Freemasonry at all times and, as in the previous example, should be constantly reminded to improve that reflection of myself. I like to think of it akin to the fact that as children, we're all on our best behavior when our parents are watching. We in turn should be representative upright citizens at all times since we never know who may be observing our conduct.
Besides, it's easier to show off :)
