Magnetohydrodynamic (MHD) mode activity in the Alfvén frequency range has been detected in the absence of energetic ions during discharges in several conventional tokamaks and spherical tokamaks, including the Tokamak Fusion Test Reactor (TFTR) and the Mega-Amp Spherical Tokamak (MAST). In TFTR the dominant toroidal mode number n was found to be zero; this is also the case in MAST discharges for which mode number information is available. The observed properties of these modes are shown to be consistent with global Alfvén eigenmodes (GAEs). Although they appear to have little or no effect on plasma performance in present-day devices, the fact that they are frequently observed in MAST Ohmic discharges suggests that they could be used as a diagnostic of plasma equilibrium parameters. In principle, they could also provide the basis for a plasma heating scheme. A possible mechanism for the excitation of the Alfvén eigenmodes in the absence of fast ions is suggested by two-fluid simulations of various tokamaks, in which high-frequency mode activity is found to be correlated with relatively long-timescale MHD events in the plasma, such as internal reconnection events (IREs) or edge localized modes (ELMs). A simple analytical model describing the excitation of Alfvénic modes by either IREs or ELMs is proposed. The coupling of low- and high-frequency MHD is predicted to be strongest for radially-extended modes: this is consistent with the low mode numbers of the activity observed in TFTR and MAST.