While many people can take care of painting a room, unclogging a toilet or even installing a light switch (after making sure the circuit is shut down), when it comes to the big stuff, it's time to call in the professionals.
Depending on the project, some electrical work requires a permit to perform anyway. There's always the threat of electrical fires or electrocution with these projects so unless you're a licensed, experienced electrician, put down the pliers and pick up the phone instead.
The destructive power of water is never so evident as when there's a leak. While you may think you have a plumbing issue under control, a licensed plumber will know how to fix an existing problem without setting off another one.
Structural renovations — tearing down a wall for example — involve more than just the wall itself. In addition to running the risk that it's a supporting wall, you simply may not know what to do with any electrical or plumbing "surprises" behind the wall.
It's important to recognize that even if you're OK with your "handyman's special" repair job, it may come back to haunt you when you decide to sell your place, and a home inspector points out issues that you may have to have professionally repaired at that time anyway.