We consider Roche lobe overflow (RLO) from a low-mass star on a nearly circular orbit, onto a supermassive black hole (SMBH). If mass transfer is unstable, its rate accelerates in a runaway process, resulting in highly super-Eddington mass accretion rates, accompanied by an optically-thick outflow emanating from the SMBH vicinity. This produces a week-month long, bright optical/Ultraviolet flare, accompanied by a year-decade long X-ray precursor and post-cursor emitted from the accretion flow onto the SMBH. Such ``Circular Tidal Disruption Events (TDEs)" represent a new class of nuclear transients, occurring at up to $1-10\%$ of the canonical parabolic tidal disruption event rate. Near breakup rotation and strong tidal deformation of the star prior to disruption could lead to strong magnetic fields, making circular-TDEs possible progenitors of jetted TDEs. Outflows prior to the final stellar disruption produce a circum-nuclear environment (CNM) with $\sim \rm 10^{-2} \, M_\odot$ at distances of $\sim 0.01-0.1 \, \rm pc$, likely leading to bright radio emission, and also similar to the CNM inferred for jetted TDEs. We discuss broader connections between circular TDEs and other recently identified classes of transients associated with galactic nuclei, such as repeating-TDEs and Quasi-Periodic X-ray Eruptions, as well as possible connections to luminous fast blue optical transients such as AT2018cow. We also discuss observational signatures of the analogous RLO of a white dwarf around an intermediate mass BH, which may be a multi-messenger source in the LISA era.