General-order equation-of-motion coupled-cluster methods for ionization potentials and electron affinities (IP-EOM-CC and EA-EOM-CC) are developed by employing a determinantal algorithm. With these, principal ionization potentials or electron affinities of diatomic molecules and the excitation energies of their ionized or electron-attached counterparts are computed across different approximations of the cluster operator and the ionization (electron-attachment) operator. IP-EOM-CC(2,2h-1p) = IP-EOM-CCSD and EA-EOM-CC(2,1h-2p) = EA-EOM-CCSD or EA-EOM-CC(2,2h-3p) prove to be well-balanced models for principal ionization potentials and electron affinities; whereas for the quantitative descriptions of non-Koopmans ionization or electron-attachment processes IP-EOM-CC(3,3h-2p) = IP-EOM-CCSDT and EA-EOM-CC(2,2h-3p) appear to be the minimal levels.