Clothing racks and perhaps associated changing rooms?
Two very different examples, actually, at least unless there is adequate privacy in the changing rooms that one can be certain that no one will be seen in a state of undress where they don't want to be seen.
I thought of my own example and I found myself thinking of quite a few examples of activity that are separated by gender. The first, and probably best, example I came up with is a sewing circle. In particular, I thought of a group of friends who would regularly hold a "stitch and bitch" session. There wasn't an actual rule that no men were allowed, but it was unstated that it was only for women, and everyone knew that the point of it wasn't really to complete those embroidery projects. It was to get together with the girls and talk about whatever it is that they talk about when we aren't around. The presence of a man would fundamentally change the social dynamics of the "stitch and bitch".
Note: I'm using "man" and words above in the modern, gender-oriented, sense. If there was a woman who happened to be a male present at the "stitch and bitch", it wouldn't disrupt the dynamics so long as the male actually behaved like a woman and was accepted as such by the participants.
But, that example, and every other one I thought of, were purely private functions. There were no laws associated with the "stitch and bitch", or at a bachelor party, or wherever.
In the past, a lot of workplaces were very gender oriented. It was felt that a woman just wouldn't be appropriate in some work environments. At the time, they didn't realize they were also segregating by sex, but people who were not sufficiently "manly" weren't always welcomed there, regardless of sex. I think everyone here would agree that it is a good thing that laws have been passed that outlaw such workplace segregation today, whether that segregation is based on sex or on gender, and whether that segregation is official policy or unofficial practice.
In terms of things that are segregated by law or by government policy, I could not come up with a reason to segregate by gender, but perhaps someone else can explain the rationale for why such places or activities ought to exist.