Pick your battles.
Your 18-month-old daughter wants to wear a pink ballerina tutu and orange rain boots to the grocery store?...that doesn't hurt anything. Maybe your 9-year-old son (like mine) chooses to wear shorts and tank tops in the winter and pants and long-sleeved shirts in the summer. Make sure he has a jacket in the winter and lots of water in the summer and he'll be fine.
Maybe your kid (like mine) pretty much only survives on peanut butter. It's easier to buy peanut butter in bulk than convince the kid to eat other stuff.
Maybe you have to watch the latest Pixar movie 24 times in a single month. It won't kill you.
If it isn't going to harm them or someone else, just let it go. They will probably grow out of the worst of it.
And for the biggest bang for the buck...Listen. Once they can communicate, it's worth your while to find out WHY they are upset or being stubborn or being a complete pain in the neck. Sometimes their reasons will make absolutely no sense to you, but to your child, that reason is not only logical but IMPORTANT. My children are tweens now, but we have established that if they can explain to me WHY something is very important to them to do/not do/have/whatever, then I will listen (without telling them that their thought process is stupid/illogical/etc) and, if nothing else, try to find a compromise. This goes back to "pick your battles".
Examples -
My then-3-year-old insisted on carrying a Mickey Mouse doll everywhere - to the store, to day care, to church. Why? Because Mickey would be scared all by himself. So, over my mother's strenuous objections, Mickey Mouse helped my son escort me down the aisle at my second wedding. My son beamed all the way down, and the pictures still make me smile.
My 12-year-old was upset when she found out I was going to order school supplies online because I hate dealing with the crowds to dig out the exact color folder on the list. She told me that the online supplies are cheap quality and she spends too much time trying to fix them. We decided I would give her the money I would have spent, she'll provide a bit of her own, and I will drop her and her best friend off at the store to be completely in charge of the school supply shopping.
It's a win-win. Tantrums averted, so Mom is happy. Children feel heard and validated, so they are happy. Children are learning the art of negotiation and compromise.
Also, buy earplugs in bulk. We keep some in the car for when they are too loud in the backseat. Easier than trying to make them shut up.