Permits Are Required: Generally things like bathroom remodels, moving existing plumbing, or adding new a new gas line for your BBQ will require a permit. A professional will know when a permit is required and the process and building codes to make sure the inspections go through.
Main Line Stoppage: Anytime the toilets are backing up into the tubs and showers the problem is most likely the main line. This usually requires special equipment that most homeowners don't typically have. While renting the equipment is possible, it is not advisable unless you have experience using it. A professional will have experience using the equipment and clearing out the main line.
Shower Valve Replacement: This can be complex and time consuming for the inexperienced do-it-yourselfer. An expert can help you pick out the right valve for your shower. The options are many and it can get confusing very quickly. There is also the possibility of damaging the shower walls in the process. A professional will know how to change the valve with the least amount of damage (if any) to your walls.
Water Heaters: Depending on this situation it is not recommended to work on your own water heater without experience or proper guidance. There are a lot of things that can go wrong during a water heater repair. An apparently simple adjustment may end up making a leak worse or causing more damage.
Tub Replacement: This type of project is a big job, even for the professional plumber. It may sound straight forward, but it is quite involved and I don't recommend it for even the handiest homeowner.
Even with small projects it can sometimes be worthwhile to call a professional. Hiring a plumber can sometimes save both time and money. Before you buy tools and invest your time, call around to find out what a pro will charge. Then you'll know just how much you can save yourself.