We didn't do much of this at all. We "knew of" some of our competitors by name and some of what they did but we didn't bother digging in, etc. I think (and this is purely an opinion) that when you become focused on your competitors or more aware, you end up being influenced whether you believe it or not. It leads to a lot of overlaps and copycat issues (see big companies competing).

By not concerning with that and concerning with building your product the exact way you'd use it to solve for your exact pain points and those of your early adopters, great things can come out of that that are sometimes planned and sometimes spontaneous.