Like Taylor, I tend to use random tools as a starting point, then edit the results to something seemingly not random. Especially noises and field recordings, where I work with whatever I'm able to capture.
I have a small modular synth, and one of the modules I have is the Zorlon Cannon, which creates series of pseudo-random gates. I use those a lot, especially as a clock source for fixed sequences so that it runs through the same eight notes, but at irregular intervals.
In terms of software, I use the probability functions on Replicant quite a lot. I also use the slice randomization on Liveslice a lot until I come across a sequence I like, then I fine tune it. I very rarely sequence MIDI, so don't use random MIDI tools much. I really like the randomizing and probability functions on the sequencer on the drumsynth plugin Tattoo, but I don't have much call to use it often given my preferred way of working.