I'm getting three cavities worked on tomorrow without novacaine. What am I in for?

Individual variance. This should be discussed with your dentist prior to him\her treating you. While there are some patients who do not require local anesthesia for fillings, & there are some very small fillings that require no local anesthesia, most patients do require something to ensure they will be comfortable for the procedure. In some cases 'sweet air' is used alone or in combination with an injection.
Why no local? Why are you not having any local anesthesia? If you elect to not use a local anesthetic, you may feel anything from a minor discomfort to an intense burning sensation. Speak with your dentist before treatment to make sure you understand all your options. Modern dentistry is usually pain free.
Novocaine or not? First of all novocaine is not used any longer but less harmful derviatives have been developed through the years to achieve anesthesia without undesired side effects, but why are you having it done without the anesthetic? Allergy, fear? Paying a penance? I personally would opt for comfortable. But, good luck.
Depends. It depends on your tolerance for discomfort. It depends on the size of the cavity bigger cavities are closer to the nerve so the cold and vibration can stimulate the nerve more. 25 years ago there was no question that small cavities would be done without novacaine. Everyone is different on how they react to discomfort. Everything we do as a dentist is uncomfortable, novacaine makes it easier.
Depends... Talk with your provider. There are many ways of treating the pain of your procedure. Figure out a plan that will work for you.