This is not a simple question, especially with regard to cats.
Many American states (not all) require rabies shots for cats, and some counties and localities require them in states that don't have a statewide mandate. Laws vary in other countries. (In some countries like England rabies is not an issue.)
There are some really horrible diseases that cats can get if they aren't vaccinated. However vaccination is a complex medical procedure, much more complex than most people realize, and it has its hazards. For cats the big risk is VAS - Vaccine Associated Sarcoma - cancers (usually fibrosarcoma) with a low survival rate.
There are worse things than cancer; rabies is one, and so is "distemper." But vaccinating a cat for diseases it's not likely to be exposed to introduces an unnecesary cancer risk.
Another factor is that there are diseases that are highly contageous to kittens but difficult to transmit between adults, such as feline leukemia. There are illnesses that can be fatal to kittens but are merely annoying to adults. And not all feline diseases are present in all geographic areas.
If that's not enough to worry about, there are vaccines that work quite well and others that aren't worth swat (The FIV vaccine is one; it's only marginally effective against only the least common of the five known strains of FIV virus) and others that cary a high risk of major side effects (for example, the Lyme disease vaccine was foisted on the veterinary community after it was discontinued for human use because it can cause severe arthritis; it can cause severe arthritis in animals, too.)
So there's no simple answer to what vaccinations a cat needs. You have to consider what diseases the cat might realistically be expected to be exposed to based on kitty's lifestyle and where it lives, how dangerous those diseases are to a cat of your kitty's age, and how effective the vaccine is. An outdoor cat in a rural area where there are a lot of diseases might need a lot of vaccinations. An indoor kitty who lives in an urban high-rise and who will never get outdoors might not need any vaccines at all.
Here are some links you might find interesting:
Posted 465 days ago