There are a number of citrus and lanolin based hand cleaners out there do a great job and aren't very hard on the skin. It really depends on what I'm dealing with. Citrus works great on paints and oils, lanolin works on oils, and good old soap with abrasive, like ground peach pits works on things that don't dissolve well like inks and dyes.

For some things I do a first wash with olive oil which loosens and dissolves what's on my hands, than a few soap and water washes to get the olive oil off. The olive oil trick only works well if it's done before water washing.

Often it isn't about getting my hands looking clean, but getting the smell out like after changing a fuel oil filter. Nothing I've ever found gets the diesel fuel odor off, but the juice from a fresh lemon hides it pretty effectively.