Ear wax is a normal physiological substance which the ears generate to keep themselves clean. Modified sweat glands in the ear canals make the wax which travels along the ear canal to the outside world. It is carried on the backs of squamous epithelial skin cells which form in the centre of the ear drum and migrate outwards. This is the ear's self cleaning mechanism; because of this you don't need to clean the ears yourself; they will do it on their own.
Sometimes ear wax, dirt and dead skin can build up in the ear, causing deafness, tinnitus, water logging and ear infections. In this situation the ears may need to be syringed or suctioned cleaned. If ear buds are pushed into the canal it can push muck back up the canal. This causes problems because the ear's self-cleaning mechanism breaks down.
If people with excessive wax need to use ear plugs then molded versions tend to be better. They are wipe-clean, antibacterial and non-porous, making them more hygienic. ZenPlugs website has a range of useful articles on ear problems and how to manage them. Their ear plugs are antibacterial and last for years of normal use. This makes them more economical in the long run compared to foam and wax ear plugs which need to be replaced after a few uses.