I mostly use watercolor pencils, so I always have to mix the colors on the paper. Which I guess is just as well; I'm terrible at judging how much liquid/etc to use, so I'm pretty sure that if I did use palettes I would always have too little or too much.
It tends to be a combination of both for me depending on what im attempting to do.. Some things like skin tone require that the under tones are painted first then the main tone is glazed on top. However the main tone often requires one or more colors.. (one of my faves is naples yellow hue with cobalt violet for a lovely pale skin tone... or cadmium yellow hue with cad red dark( A VERY SMALL AMOUNT) also makes a great skin tone but its really what ever you like)
I have about a million paint boxes and like five posy pallets (these lil suckers.. tho mine only have 7 wells each >>>[link] ) so i have lots of room to play around and see what works.
I mix most of my colors on the palette, since the final colors look more transparent and lucent when they are painted in few layers. A sheet of used watercolor paper is good to try out the mixed color before actually painting with it.
I know it's a generally accepted fact that it's better to mix paints on paper and not on the palette. But control freak that I am, I want to have some idea of what the final color will look like and so mix on the palette more than I mix on paper.
I do love paper-mixed colors, though. They're so complex and vibrant.
I bought a new watercolor kit recently, but I don't want to stain it with paint (yeah, I know it can be easily cleaned) so I've been mixing all my colours on the paper lately, painting layer by layer. I've never done this before, but I like this technique.