I referred to my motherboard's manual often when constructing my PC because every motherboard is different, and I wanted to get a really good understanding of its layout and such before I attempted to install anything on it or plug anything into it. I still look at it from time to time just because if I'm curious about something, it's a lot easier to pop out the manual than to pop open the computer case. With other tech though, I don't usually need a manual as most of it is pretty obvious.
As for non-tech stuff, I'm not much of a manual person. If I'm trying to put something together, like a piece of furniture that requires assembly, I usually look at the manual briefly just to get a basic overview of how it's supposed to fit together, but I don't follow it religiously.