That is a pretty broad topic. Carbon composition (CC) resistors are less affected by RFI so we traditionally used them as grid and plate stoppers, which stop RF. But as PB mentions the CCs we were able to get were fairly fragile where the lead entered the resistor body and they would often get broken there. So we switched to carbon film which is also pretty good at RF rejection and is non-inductive as well.
For some apps, say like an RIAA filter in a phono preamp, precision is important. In these cases metal film resistors, which can be trimmed to a tight tolerance like 0.1%, are ideal. Some feel this type of resistor construction may color the sound less than other types and it is often spec'd for situations where the audio signal passes thru the resistor like an attenuator.
In applications like power supplies and plate and cathode resistors there can be a lot of current going thru the resistor and/or a large voltage drop. For these apps we need a resistor that can handle a lot of power and thus a lot of heat. Something like a wirewound ceramic or a metal oxide resistor often is appropriate here.
All of this said, sometimes we use a resistor value or type because it is a part we already stock for other kits and it is a good fit for the new application as well. We go through thousands of 220 ohm CF resistors.
