I stim almost all the time, by rolling a rubberband between my fingers. My thoughts do get a little more haphazard when I'm not doing this; I always feel like I need to be doing something with my hands.
It's interesting to think of all the different actions that can be classified as stimming. Sometimes I think my walks are a form of stimming. I listen to my music and walk, and this is the time I am able to think most clearly. Whenever I'm having a thought I like, I run (or at least feel an urge to run).