Feline Panleukopenia (FPV) - an extremely possibly fatal contagious virus that causes severe gastroenteritis.
Feline Rhinotracheitis/Feline Calcivirus (FCV) - viruses responsible for cat flu, can be fatal.
Rabies - almost always fatal and easily spread from animal to human.

Other vaccines your veterinarian may suggest:

Feline Chlamydophilosis - a type of bacteria that causes conjunctivitis(swollen red watery eyes) in cats, it is spread by direct contact between cats and is often seen in kittens or in multi-cat households
Feline Leukemia Virus(FeLV) - the leading viral killer of cats, it is transmitted by direct contact between cats. The vaccination has some controversy so do your research & discuss whether this vaccination is right for your cat with your veterinarian

Fleas - Fleas are easily preventable by treating your cat regularely with a spot on treatment such as Revolution or Advantage, which you can get from your veterinarian (Do not use dog treatments that contain permethrin as it is fatal to cats). If you haven't already started a flea control regimen, I strongly suggest you consider it. It is a lot easier to prevent fleas than it is to treat them. If your cat is frequently scratching it could be a sign that it has fleas. If you think your cat has fleas, look through your cats fur or comb it with a flea comb. If you notice little black spots(usually behind the ears or on the back at the base of the tail) collect it and place it on a damp paper towel. Rub the dirt between 2 sides of the paper towel, if it is flea droppings it will turn to a reddish brown color. If you have a bad infestation you may see the fleas, or notice bites on yourself or others in your home. If your cat does have fleas, treat your cat immediately (spot on treatments work best). You will also need to treat your entire house, including your pets bedding, carpets an soft furnishings. Retreatment may be necessary

Ear Mites
Ear mites are transmitted from one infected pet to another. Symptoms your cat has ear mites is constant scratching at its ears and shaking its head. If you look in your cats ears they will appear to be dirty. If you suspect your cat has ear mites contact your veterinarian who will be able to give you some medication to treat it. They will most likely want to see your cat to confirm the diagnosis.

Worms (Intestinal Parasites)
It is very common for a cat to have worms, but they rarely show symptoms unless they are heavily infested. Symptoms can include weight loss, vomiting, diarrhea and bloating. Some types of worms can be passed from cats to humans. Because of this it is a good idea to regularely have your cat treated for worms. You can get medication to treat your cat from your veterinarian.