What do you mean by the term "replace"? Does your question ask whether a circuit that would normally use an opamp could be designed without and opamp, or does your question ask whether another component(s) can be placed in an existing circuit in place of an opamp?
A few years ago I replaced a broken high speed opamp with a discreet transistor-only amplifier because I didn't have the patience to wait for a replacement high speed opamp to me sent to me.
As a lab project while in school, I designed and built a complete home stereo amplifier channel with nothing but CMOS 4069 unbuffered inverters. Phono cartridge input, RIAA equalization, treble and bass tone controls, and a BTL class D output stage. Limited bandwidth, unimpressive distortion, and not much speaker power, but it did work.
As AK demonstrated, there are ways around using an op-amp, but there is no such thing as one component that can replace an op-amp. I can imagine using a single bjt base and emitter as a differential input, but the output...how can one, single, collector do all the things an op-amp does?