Do homeschoolers usually take vacation at the same time as local schools do?

Interesting question. The nature of my home schooling (autodidact-ism that I didn't start until I dropped out in the 10th grade), meant that my learning was more ad-hoc, and as such I had neither formal curriculum, nor a schedule. That said I tended to take more breaks when my friends were on breaks, because there's not much point in breaks during the day when all your friends are still in school. On the other hand a lot of what I was studying/teaching myself was stuff I was passionate about so it didn't truly subside even through "breaks".

In our area, summer is hot enough that unless you're actually traveling somewhere, it is not an ideal time to be off school. So we usually did school in the summers and took our breaks in the spring or the fall instead.

When the older children reached college, though, we switched to summer breaks so that everyone would be off at the same time.

We don't do vacations from our family projects, because we are outside of the whole "job-class-leisure" grid. However, because many people travel during the summer, and take breaks during the winter holiday season, our group events such as math clubs stop during these times.

In our home, we certainly take vacations, although not always at the same time as our local public schools do. Actually, the ability to be flexible about when to take time off is one of the benefits of homeschooling. For example, our family has a vacation cottage we share with lots of cousins. Since we don't need to be home to "start school" in early August (like many school systems do) we have been able to enjoy the end of summer at the lake.

We do, however, find that the holidays and teacher workdays in the local schools can provide opportunities for our kids to get together with friends who don't homeschool. We will often take off the same days or have a light workload on those days to take advantage of the opportunity.