With the discovery of ever smaller and colder exoplanets, terrestrial worlds with hazy atmospheres must be increasingly considered. Our Solar System's Titan is a prototypical hazy planet, whose atmosphere may be representative of a large number of planets in our Galaxy. As a step towards characterizing such worlds, we present simulations of exoplanets that resemble Titan, but orbit three different stellar hosts: G-, K-, and M-dwarf stars. We use general circulation and photochemistry models to explore the circulation and chemistry of these Titan-like planets under varying stellar spectra, in all cases assuming a Titan-like insolation. Due to the strong absorption of visible light by atmospheric haze, the redder radiation accompanying later stellar types produces more isothermal stratospheres, stronger meridional temperature gradients at mbar pressures, and deeper and stronger zonal winds. In all cases, the planets' atmospheres are strongly superrotating, but meridional circulation cells are weaker aloft under redder starlight. The photochemistry of hydrocarbon and nitrile species varies with stellar spectra, with variations in the FUV/NUV flux ratio playing an important role. Our results tentatively suggest that column haze production rates could be similar under all three hosts, implying that planets around many different stars could have similar characteristics to Titan's atmosphere. Lastly, we present theoretical emission spectra. Overall, our study indicates that, despite important and subtle differences, the circulation and chemistry of Titan-like exoplanets are relatively insensitive to differences in host star. These findings may be further probed with future space-based facilities, like WFIRST, LUVOIR, HabEx, and OST.