I caught chickenpox in 1st grade, when it was going around at my school. Gave it to my sister who was a toddler at the time. Months later, I came down with measles (fortunately a mild case). I can't remember if I gave that to little sis, but I doubt it. At least I don't recall her being sick at the time, and I remember us both having chickenpox quite clearly.
I can't remember when my sister had rubella (we called it German measles back then), but I had it during my freshman year of high school during what I later learned was the last major outbreak of that disease in the U.S. prior to the vaccine coming out. Rubella is typically a mild disease, but if a pregnant woman catches it early in pregnancy, it is likely to cause miscarriage or very severe birth defects.
Neither of us ever had mumps (the 2d M In the MMR vaccine), and I've found myself wondering if I need to get that vaccine now that people are being advised by the federal freaking government to skip vaccinating their kids. Fortunately, I live in a blue state where people are less prone to being antiscience and the state has laws in place requiring vaccinations for kids to attend school.
Just one small correction to your comment: the chickenpox vaccine was not licensed for use in the U.S. until 1995 (although it was in use earlier in Japan). When my daughter was little, chickenpox epidemics were still a routine thing, and she caught it before the vaccine came out. It wouldn't have been a big deal, except that she gave it to her dad, who had somehow missed catching it as a kid, and it made him much, much sicker than it did her!