Context. This paper is part of a series involving the AMIGA project (Analysis of the Interstellar Medium of Isolated GAlaxies), which identifies and studies a statistically significant sample of the most isolated galaxies in the northern sky. Aims. We present a catalogue of nuclear activity, traced by optical emission lines, in a well-defined sample of the most isolated galaxies in the local Universe, which will be used as a basis for studying the effect of the environment on nuclear activity. Methods. We obtained spectral data from the 6th Data Release of the Sloan Digital Sky Survey, which were inspected in a semiautomatic way. We subtracted the underlying stellar populations from the spectra (using the software Starlight) and modelled the nuclear emission features. Standard emission-line diagnostics diagrams were applied, using a new classification scheme that takes into account censored data, to classify the type of nuclear emission. Results. We provide a final catalogue of spectroscopic data, stellar populations, emission lines and classification of optical nuclear activity for AMIGA galaxies. The prevalence of optical active galactic nuclei (AGN) in AMIGA galaxies is 20.4%, or 36.7% including transition objects. The fraction of AGN increases steeply towards earlier morphological types and higher luminosities. We compare these results with a matched analysis of galaxies in isolated denser environments (Hickson Compact Groups). After correcting for the effects of the morphology and luminosity, we find that there is no evidence for a difference in the prevalence of AGN between isolated and compact group galaxies, and we discuss the implications of this result. Conclusions. We find that a major interaction is not a necessary condition for the triggering of optical AGN.