Oh we do both, depending on the complexity of the project. DH installed all our new ceiling fans (3) b/c he knew it was something he could handle. But adding a new outlet, we called a professional. Electricity really is something I would rather leave to a professional, anyway. Plumbing is the same thing. DH and his dad moved my washer in my basement laundry room to better configure our space--they just added and extended the water pipes along the same wall. But when we needed to hook up a new laundry sink and add a vent and tap into the drain, we hired a plumber. DH installed our new garage door openers himself but we did hire a contractor to install our new garage doors. DH put in our backyard fence himself but his dad helped with the digging and cementing the posts.
DH will help friends/family with projects but is reluctant to just do something by himself at another person's home as he is not an expert. So when our neighbor saw he installed our ceiling fans and asked if DH would mind doing that for his house, DH said "I will show you how and help you, yes." But he didn't just go over and do it all by himself.
We have saved money doing things ourselves but I also think we have saved money by hiring a professional. It took the plumber a few hours for the laundry room project but it may have taken DH days to figure out how to get everything just right.
Also, I am concerned about proper building and remodeling codes. Sometimes to get things to "code," a professional has to be involved.