I have used food processors for more than 30 years and would really miss it. The first was a Braun that I got with S&H Green Stamps when we lived in Florida, and after more than 25 years a part broke and could not be replaced. I bought a Kitchenaid and the handle broke after only about a year, guaranteeing that I will never again buy that brand of anything! I got another Braun and I'm happy with it.
I use it several times a week, and sometimes several times in a day, especially around the holidays. It saves time, and the parts go into the dishwasher, so there's no complaint about clean-up.
Let's see how many things I can think of that I do:
Mixing the wet ingredients for banana bread.
Making hummus and other dips.
Making a strawberry health shake (1 cup buttermilk, 2 cups frozen berries, a bit of Splenda).
Pumpkin shake (vanilla ice cream, pumpkin pie spice, canned pumpkin)
Orange or chocolate buttercream frosting. Some other flavors come out tasting a little raw, but those two are great.
Pureeing all sorts of things.
Mine has a juice reamer, which I don't often use because there are just the 2 of us, but if I wanted a lot of juice, that would be good.
Pie crust. Don't over mix it!
Grating carrots.
Grating cheese.
Slicing potatoes for scalloped potatoes.
Chopping nuts or almost anything else that needs chopping or mincing.
Chicken salad (or beef or ham salad)
Quick bean soup: Puree a can of beans and cook it with another can of beans left whole plus whatever other ingredients your recipe calls for. It gives the soup a great texture in a hurry.
Before I had my bread machine, I used the food processor to "knead" yeast dough, and it works pretty well. I would recommend looking for a recipe that's tailored to that method because there is limited capacity. I don't remember what recipe I used.
Oddly, I don't usually use it for deviled eggs because I usually only make a few and find it easier to drop the yolks and other ingrds. into a Seal-a-meal bag, work them around by hand and then cut a corner off to fill the eggs - less mess.
I can't think of any others off the bat, but you get the idea. I would rank it right up there with the microwave among things I appreciate in the kitchen. At first you will tend to follow your old habits and tend to forget about it, but if you remind yourself to consider whether something could be simplified with this machine, you will be surprised how often it could. It's best to have it out where you won't have to do too much digging around to get at it. Read the manual and start by using recipes in it first to familiarize yourself. Have fun.