Anything that comes into contact with bodily fluids (blood, plasma, mucus, semen, etc.) that cannot be sterilized must be disposed of. But you can't throw bio-hazard materials into a regular trash can, because then it could harm someone it comes in contact with at the waste management facility, or end up in the water supply or on a beach somewhere. Medical waste must be discarded in a separate bag or canister marked clearly as a biohazard.
Needles of any kind must be discarded in a sharps container. A sharps container is a plastic container, usually red, with a biohazard symbol on the outside. Just like the one in the doctor's office labeled "hazardous waste". The entire container is disposed of once it is full.
Things used by tattoo and piercing artists that qualify as hazardous waste (after use) that cannot be sterilized include (but are not limited to):
Tattoo needle sharps
Plastic protective covers (used to cover the tattoo machine, cord, soap bottles, etc.)
Ink caps and leftover ink in caps
Any leftover ointment removed for use
Except for the actual sharps on the end of a tattoo needle bar, anything metal can be sterilized in an autoclave and reused. This includes piercing needles, tapers, needle bars and tattoo machine tubes.