My experience is that there are people who do resist annexation, usually strictly because of taxes. There are also typically people who want to be annexed, usually because they want the enhanced services that the city provides.
Obviously, specific circumstances will affect how people feel. I don't personally know of situations where annexation represented a downgrading of services, but I'm sure they exist. Usually the resisters claim that they don't want the enhanced services (often including better-funded schools, access to park districts and libraries, etc.).