Dust mites are a real danger to your health, and that's why you should air all mattresses and bedding every day. You won't see dust mites (they're only about a quarter of a millimetre long) but they cause both short-term problems (rashes, inflamed eyelids, etc.) and long-term (allergic reactions, asthma, susceptibility to viruses, etc.).
Sweat accumulating in bedding and mattresses is another problem. The average person leaves 26 gallons of sweat in their bedding each year.
Mattresses and bedding accumulate fungal spores, bacteria, dander (from pets), pollen, soil, lint, chemical finishing agents and colourants (used in bedlinen manufacturing), and various body fluids (sputum, vaginal, and anal excretions, urine, skin cells, as well as sweat).
Sunlight is a brilliant answer to all the above and if you're lucky enough to live in Scandinavia, Australia or wherever you have plenty of the stuff, then putting as much bedding as you can outside each day is a brilliant answer. However if you're in the UK or other less sunny clime, you need to employ other remedies.
Airing your mattress and bedding each day is an absolute must if you want to stay healthy. The bed should be stripped down to the mattress as soon as you get out of bed. Take pillows off the bed as well, and put them somewhere (for example on a bedside table) a different way up from how they have been lying on the bed. Hanging the duvet over a door (as another poster mentioned) is a great idea. Shaking sheets out of windows or outside a house door, preferably after the sheets have cooled, is excellent.
Natural bedding (wool, silk, cotton, feather, buckwheat) is far better at repelling dust mites and shaking off other nasties than synthetics. Everything should be renewed periodically (a two-year-old pillow may consist of up to a third of mites and their faeces and other sheddings, mould spores, dead skin and other lovely things). Try buckwheat pillows - not only are they not natural homes for bugs, they're super-comfortable, supportive, airy, and you can just add more buckwheat husks periodically - which actually works out cheaper than constantly buying other types of pillows.
Sheets and pillowcases should be changed once a week (unless someone is ill in bed, in which case it's every day). Duvet covers should be changed every week to ten days. Natural duvets should be aired in full sunlight (beating and turning during this time) several times a year - rather than being washed or cleaned. Synthetic duvets can be washed - but they do tend to give off chemicals which may cause or exacerbate allergies. (No one knows the long-term effects of inhaling all those chemicals every night because studies simply haven't been done.)
Using natural substances such as bicarbonate of soda and vinegar, as one poster mentioned, to help clean and disinfect would seem highly sensible. However using chemical substances such as fabric conditioner may, again, cause long-term problems such as allergic reactions. These substances are also often 'sticky', which can cause nasties to clog up and stay where they are in the bedding or mattress.
Whether or not vacuuming your mattress is useful depends on your mattress composition. Natural mattresses (made of cotton, silk, wool, etc.) should be turned regularly (once a week, alternately top to bottom and side to side) and are unlikely to need vacuuming. Synthetic mattresses may or may not need turning but are likely to benefit from vacuuming. Any vacuum used will need to be very strong; handhelds and battery-vacuums are unlikely to provide sufficient suction. Vacuuming pillows as well (unless they're, for example, buckwheat) is a good idea - but at least a separate nozzle attachment (if not the entire vacuum, which is preferable) should be kept for this purpose.
Whether or not domestic UV light cleaners for mattresses work, I simply can't find out. Are they sufficiently strong? If you've got the money, it certainly wouldn't seem to do any harm and dust mites near the surface of the mattress would be sorted out at least.
As you can see, I'm passionate about beds and bedding(!). A good night's sleep is one of the keys to good health - but we spend longer choosing the design of our bed than we do on choosing the right bedding and looking after it...