Here (Norway) it's whenever it involves the work on the mains panel or on unterminated power wire. You can change ceiling fixture if it has a clip in power socket, you can of course change lightbulbs (doubt it's licensed anywhere in the world), you can even install electric flooring that clicks to connect. You can't do anything that requires tying or soldering power wire together, and you can't install hidden cabling/channels and fixtures yourself (fire safety reasons).
In some cities you would need a permit to replace an outlet. And only licensed electricians are allowed to get permits. In some cities bad wiring jobs don’t just burn you own house down, it’ll take the neighbors house with it. So it’s not just your butt on the line if you screw up.
People do that anyway, just that you'll have tough luck if it comes up in an insurance case. Or worse if you are in a condo and other people suffer.
Wiring and outlets are simple enough, but you wouldn't believe peoples' capacity to botch things up. They'd connect a ground pin socket in place of non grounded one without changing the wiring, or use incorrect section wire, or with incorrect insulation type for in-wall application, or they'd replace a charred outlet without trimming the sooted part of wire. Enough nuances to avoid amateur work.
So can you change an electric outlet? That means turning off the individual circuit (or mains if you are paranoid) then opening, disconnecting, connecting a new one.
What about installing a ceiling fan? Assuming the wiring is already there.
You can put exterior signal cables yourself. The wall conducts for such cables still have to be put in place by electricians I believe, but not 100% sure.
Most likely you can freely do the installation yourself but it has to be connected or maybe just cross-checked and then signed off by a certified electrician to become a legal installation. That's what homeowners commonly do to save money.
