This is something that I am asked on a daily basis and it really depends on two things: (1) the type of appliance, and (2) appliance use.
The general rule for fires or appliances that burn wood only, is to have them swept twice a year (midway and end of season). For those that burn smokeless fuel, having them cleaned once a year is advised. Liners also need sweeping, just the same as chimneys!
For appliances or back boilers that heat water or radiators, it is recommended that you have them cleaned 2-3 times a year when in use.
Another important thing to remember, is that if you do not maintain your chimney or liner in line with the sweeping recommendations, in the event of a chimney fire and damage to your property, your insurance company is unlikely to cover you.
The pictures below are of unswept chimneys. As you can see, soot, sticks and even birds nests build up in the chimney - all of which increases the potential risk to you and your families.
Keep safe and keep those chimneys swept!