1. Removing Asbestos
First of all, do you see how those guys are dressed? That is a smoking gun that removing asbestos is not something you should do yourself. It's dangerous to your health and what dollar value is worth living a health life? To quote the United States Department of Labor:
"Breathing asbestos fibers can cause a buildup of scar-like tissue in the lungs called asbestosis and result in loss of lung function that often progresses to disability and death. Asbestos also causes cancer of the lung and other diseases such as mesothelioma of the pleura which is a fatal malignant tumor of the membrane lining the cavity of the lung or stomach. "Hire a professional, please.
2. DIY Tree Removal
3. Major Home Structural Changes
Before you go all hulk on your house, take a second and think "there might be something really important that I don't know." Demolition is really dangerous in and of itself but it can create far reaching problems you didn't anticipate like weakening the structural integrity of your home. Also think before doing major bathroom jobs, building a deck, and any other large scale home improvements. There is probably permits and licensing laws that unqualify your handy man (or handy woman) status for certain things. An experienced residential contractor can get the job done professionally and safely.
4. DIY Home Electrical Work
If you get shocked by electricity it wont be this cute. Plus there are permits and other requirements you probably don't meet to be able to pull off electrical work. You could even create a fire or cause some potentially dangerous event weeks or months down the road. You don't want your house to be a ticking time bomb, call an electrician!