A generic search for anomalous production of events with at least three charged leptons is presented. The data sample consists of pp collisions at TeV collected in 2012 by the ATLAS experiment at the CERN Large Hadron Collider, and corresponds to an integrated luminosity of 20.3 fb(-1). Events are required to have at least three selected lepton candidates, at least two of which must be electrons or muons, while the third may be a hadronically decaying tau. Selected events are categorized based on their lepton flavour content and signal regions are constructed using several kinematic variables of interest. No significant deviations from Standard Model predictions are observed. Model-independent upper limits on contributions from beyond the Standard Model phenomena are provided for each signal region, along with prescription to re-interpret the limits for any model. Constraints are also placed on models predicting doubly charged Higgs bosons and excited leptons. For doubly charged Higgs bosons decaying to e tau or mu tau, lower limits on the mass are set at 400 GeV at 95\% confidence level. For excited leptons, constraints are provided as functions of both the mass of the excited state and the compositeness scale I >, with the strongest mass constraints arising in regions where the mass equals I >. In such scenarios, lower mass limits are set at 3.0 TeV for excited electrons and muons, 2.5 TeV for excited taus, and 1.6 TeV for every excited-neutrino flavour.