A multi-vitamin would probably be a good idea but, I would get to a doctor for a good overall checkup. If you really feel that your immune system is weak there could be some underlying health problems causing it.
One possibility is allergies. They can mimic the symptoms of a cold but usually last longer. Does it seem that the symptoms come on at certain times of the year or when you are around a certain type of area, pollen prone, cats, dogs, anything at all that you may be sensitive to?
If it isn't allergies or some other health problem then one of the simplest ways to prevent catching a cold or the flu is to be very conscientious about washing your hands. Always wash your hands before you eat anything. Wash your hands after you handle anything that someone else may have touched - doorknobs, phones, money, keyboards, mice (computer kind), handlebars, weights, cardiomachines and of course after you go to the restroom. Also wipe down the community gym equipment with a disinfectant wipe before you use it, people may think you are anal but it beats being sick.
Anytime you work out, you lower your immune system somewhat, especially when lifting weights or when you up the intensity of your workout. I read somewhere (Men's Fitness or Muscle & Fitness) that studies have shown a decreased immune response for up to 48 hours after a good weightlifting workout was pretty normal. If you do a good workout, then climb on a piece of equipment that someone else with a cold had used, you are just asking to catch it.