The Dumplings are now in their late teens, so a real party wouldn't really fit. When they were younger, we did a small-scale party - a few child-chosen friends (no gifts, please), and a minor planned activity: swimming, bowling, etc. Sleepovers when they were at that stage. Then a family meal of the child's choice. Either home or restaurant. Nowdays, I use birthdays as an excuse for a really special gift I can't really afford. Last year it was a saxaphone for YoungSon, some ridiculously expensive kitchen tools for BigGirl for example. We still always have a special family dinner to celebrate.
We give each other small gifts all year - a cool toy or book I come across, craft supplies to share. We don't really do gift giving as an occasion. It seems to detract from the fun - expectations and disappointment, a thing-oriented mood, rather than experience (fun) oriented.