I like the added control of mixing my own chemistry, the greater choice of formulas, and the ability to mix the amount that I need when I need it, so there's less waste and my developers are fresh. In general I find it less expensive to mix from bulk chemicals for the quantities that I use, and some of the formulas I use aren't available commercially.
Film and print developers that I use regularly are ABC pyro, Michael A. Smith's amidol formulas for Azo/Lodima and for enlarging papers, Ansco 130, and Paul Farber's Acufine-like formula.
Occasionally I experiment with others, just to see what they do, and sometimes I make albumen prints. I've also gone through the occasional monobath phase when I've been particularly limited for working space.
It's not as interesting to experiment with stop baths or fixers, though for some processes I use plain hypo, or I'll use a 1% sodium metabisulfite stop with an alkaline fix.