As a child, I had a couple of parties with friends but for the most part, my mom just baked my favorite cake.
Once we had kids, my mom would have a special Sunday dinner for her grandkids for their birthdays. This continued until my sister ruined it when her twins turned 17. A long story I won't go into but we don't do birthday dinners at grandma's house anymore because of it.
Joe and I usually go out to dinner for our birthdays since we were born 24 hours apart. We used to go to the State Fair since our birthdays are during it but haven't the last couple of years. For the kids, when they were young, we had family parties. Once they started school, we had their friends over. I used to fix their favorite meal for dinner and bake the cake of their choice. But once they got older, we began going out to the restaurant of their choice, usually one that would sing "Happy Birthday" to them. And when they got older, they wanted store bought cakes, so I just let them pick what they wanted.
Carol had her 18th birthday party Sunday night. She loves Batman so we had Batman everywhere, even her cake has the Batman symbol. We cooked hamburgers and sent them on a scavenger hunt where they had to collect things plus take group pictures doing stuff. They came back and played games and just hung out. Her friends are such a great group of kids!