The jet structure in gamma-ray burst (GRB) sources is still largely an open question. The leading models invoke either (1) a roughly uniform jet with sharp edges or (2) a jet with a narrow core and wide wings where the energy per solid angle drops as a power law with the angle θ from the jet symmetry axis. Recently, a two-component jet model has also been considered, with a narrow uniform jet of initial Lorentz factor Γ0 ≳ 100 surrounded by a wider uniform jet with Γ0 ∼ 10-30. Some models predict more exotic jet profiles, such as a thin uniform ring (i.e., the outflow is bounded by two concentric cones of half-opening angle θc and θc + Δθ, with Δθ ≪ θC) or a fan (a thin outflow with Δθ ≪ 1 along the rotational equator, θC = π/2 + Δθ/2). In this paper we calculate the expected afterglow light curves from such jet structures, using a simple formalism that is developed here for this purpose and could also have other applications. These light curves are qualitatively compared to observations of GRB after-glows. It is shown that the two-component jet model cannot produce very sharp features in the afterglow light curve due to the deceleration of the wide jet or the narrow jet becoming visible at lines of sight outside the edge of the jet. We find that a "ring"-shaped jet or a "fan"-shaped jet produces a jet break in the afterglow light curve that is too shallow compared to observations, where the change in the temporal decay index across the jet break is about half of that for a uniform conical jet. For a ring jet, the jet break is divided into two distinct and smaller breaks, the first occurring when γΔθ ∼ 1-2 and the second when γθc ∼ 1/2.