Three autopilots or AFCS give "Fail Operational" conditions - a faulty channel is automatically detected by comparison to the two serviceable channels. The two channels then become "Fail Passive", where a disagreement between the two indicates a fault but cannot discriminate which channel is faulty. In general, you can perform Cat III autolands with a Fail Operational system but are restricted to Cat I or II with Fail Passive.
Most of these current autopilot models are ground tested using BITE and the old practices of full autopilot checks lasting a couple of hours are gone. It is therefore necessary to check each channel by regularly using it in flight, since much of the automatic internal monitoring is only performed in flight conditions. Boeings have a test called 'MCDP Test 40' that appears to be a full check out, but this is a fallacy. That is the reason why operational policy is set to use different autopilots on different sectors - to ensure that they will be fully functional when you really need them. You should ideally be using all three channels regularly. Someone mentioned using only the centre channel: if you are on a Boeing (others too, but I'm mainly familiar with Boeings) and each pilot uses the on-side Flight Director then all three channels are being monitored, but you should still check the servo feedback loops regularly by using channels one and three.
**********************************
Through difficulties to the cinema