Humidity is a major enemy of paper, as being hygroscopic, paper naturally absorbs moisture from the atmosphere. This causes the paper to expand as it dampens and contract as it dries - possibly resulting in cockling (rippling of the paper). Moisture also promotes the growth of mould particularly if the artwork has been framed with the glass directly touching the paper as this encourages condensation to form.
Light is another danger to be aware of as all light fades works of art on paper. Fading cannot be entirely stopped by subdued lighting but obviously the stronger the light exposure then the faster the fading will occur. Avoid hanging any artwork in direct sunlight particularly as the Ultra-Violet (UV) rays can be very harmful. Fluorescent lights are also a strong sources of UV rays. Display your artwork as far away from direct light as possible and consider using UV Protective glass for any valuable or treasured pieces.
It is not a good idea to hang artwork directly above heat sources, such as radiators, as the increased airflow, caused by the warm air rising across the face of the artwork, can help to carry pollutants and the greater fluctuations in temperature when the heating switches on and off can encourage cockling.
The hanging cord/wire on the back of the frame should be inspected annually for signs of damage or weakening, paying particular attention to where the cord/wire crosses wall hooks or support rings on the frame as these areas are the most likely stress points
Consider having your most important/treasured artwork inspected periodically, say every 5 years, by an experienced framer. Any early signs of potential problems can be picked up and corrective measures taken to prevent any permanent damage.