The high energy programme of the HERA collider ended in March 2007. During the whole HERA programme, a combined total integrated luminosity of 1 fb$^{-1}$ was collected by the H1 and ZEUS experiments. In this context, an overview of the most recent results of both experiments concerning searches for new physics is presented. The topics covered are searches for contact interactions, leptoquarks and excited leptons, as well as studies of the isolated lepton and multi-lepton topologies, and a general signature based search.