You don't always need a mixer but it makes your life easier. Instead of a mixer, depending on the preparation you can use a whip, spatula and/or your hands.
STAND MIXER
My stand mixer is really convenient, especially for making dough. No need of arm muscles and I don't make too much of a mess. The shape of the bowl doesn't always make it easy to make small batches.
HAND MIXER
I used to have a hand mixer. I burnt its cable on the stove when making buttercream...
I liked my hand mixer and am thinking of getting a new one. It requires a little bit of arm muscles and I sometimes make a mess when using it but I find it useful for smaller preparations. It's also necessary to make chocolate glaze.