Inappropriate urination and defecation in a previously behaved animal may be early symptoms of a physical problem that could anything from intestinal infections, parasites to liver/kidney disease or disorders, or urinary tract infections (bacterial, viral, etc). Making sure it's really just a behavior problem means you need to have your companion checked out at the vet first. When the results come back 'clean' - you can start working on behavior modifications.
Which may not be as easy as just having an infection treated
You can look into multiple possible causes for inappropriate soiling here:
If it's a behavior problem, new activity in the house, new people, even new furniture, tension, excitement, or holidays could be causing the pet stress, feeling insecure and unsure. The new, inappropriate habits could also be an attempt to dominate a perceived threat.
Be sure to clean up the scent completely (remember, they have more than 200 million scent receptors to our meager 5 million!) and start increasing praise for their going in appropriate places as they usually do. Just the increased attention and removal of previous scent should make a big difference quickly.
When it comes to cats, urinary problems (even when presenting with inappropriate pooping) may quickly turn into blockages. When this happens, it's a medical emergency, you have a matter of hours, at best, XXXXX XXXXX the cat treated (usually operated on). It's far better to treat the earliest symptoms than be put in this position, which will cost even more if it happens at night, on a weekend or holiday.
If it's a parasite, fungal or bacterial infection, some of these are transferable to people. Keep your hands meticulously washed, litter boxes well cleaned and again, treatment sure beats the complications that may arise.
If the results of a medical evaluation indicate that kitty is just having a behavioral issue, one product to calm overly active, nervous cats is http://www.vpl.com/product.php?catmain=&mainkey=&pid=58&key=24&cat=Behavior
While we've never had to use this ourselves, we have heard plenty of good reports about it.
If you need some help in getting your companion treated, here are some options:
Don't forget to call your local Humane Society for guidance as well. If you have a Pet Smart in town, they often have the numbers for rescue organizations that may also help, at least with recommendations for where (or who ) to go.
It's truly worth doing the right thing - cats have a lifetime of unconditional love in them and ask so little in return. It's really a good deal.