It looks like it's down to Glympse and TrackMe.
I should have gone into more detail about how I'm going to use the program. I go out solo mountain biking and geocaching several times a week, and I end up in some off-the-beaten-path places (otherwise known as "the boonies"). I want my relatives to be able to know where I am in case something happens.
I need something that will call it to their attention that I am out and about, and if they need to, see where I am. So it can't be something completely passive, as Latitude seems to be.
It looks like both Glympse and TrackMe will do that. TrackMe has a slight advantage in that the map doesn't expire after a few hours and disappear. Glymse has a setting for 0, but it's not clear if that means 'don't expire'. If that is what it means, then it will work OK, also.
Thanks for the recommendations. I wish Motion-X would port their programs to Android, then I wouldn't have had the hassle of finding something else.