© 2015. The American Astronomical Society. All rights reserved.. Models are developed to simulate light curves of stars dimmed by transiting exoplanets with and without rings. These models are then applied to Kepler photometry to search for planetary rings in a sample of 21 exoplanets, mostly hot Jupiters, chosen to offer the best observational opportunity for discovering potential rings. We also examine what kinds of rings might be expected for these planets, in terms of both size and orientation, based on arguments involving the host planet's equilibrium temperature, its likely obliquities, and the formation and stability of possible ring systems. Finding no evidence for rings, for each of the 21 studied planets it is determined on an observational basis which potential rings can be rejected out of a representative set of fiducial rings, varying in both size and orientation. For 12 of the 21 planets, we determined that Saturn-like rings could be ruled out for at least certain orientations. Additionally, the detectability of rings is studied, and it is found that ringed planets with small obliquities (roughly 5°-10°) can yield large signals, which is encouraging for future work, since such small obliquities are expected for hot Jupiters.