Yes, a party for every birthday. It might be a special dinner, cake, ice cream and balloons with immediate family at home, at Chuck E Cheese, a pool party with BBQ, pizza, movies and a sleepover, but always something.
Growing up I had one "party" when I turned 6, being the eldest of 11 children I knew why, money. But each and every one of us always had our choice for dinner, a cake (the twins each got their own cake, Dad always said they were two different people), ice cream or jello and some gifts.
As the parent, you set the tone. Don't make them $400 dollar mini-extravaganzas if you don't want to. My soon-to-be 4 year old is in preschool and wants a Jake and the Never Land Pirates party, he's getting one, but I love doing them, as I love the challenge of saving money on them, lol. I'm printing the invites off Spoonful (Disney), baking the treasure chest cake, using the candy "treasures" (aka candy necklaces and bracelets from the $.99 Cents Store, Ring Pops, and gold wrapped chocolate coins) in the cake for the goodie bags, making "spyglasses" from paper towel rolls covered in pirate scrapbooking paper, and adding some glow stick bracelets ($1 for a canister with 15 of them at Target) to round the bags out. (I might cave and buy or make bandannas.) We're having it at a nearby park (free entertainment and no time constraints) and I bought his Jake toys for gifts at 70% off at Target the end of January. I am serving some food, pepperoni bread, fruit skewers, and pirate tea, but the party isn't costing me hundreds of $$$, and everyone will hopefully enjoy it.
Tell your children what you can and will comfortably do for their birthdays and stick to it. You're not being mean.