We show how accretion rate governs the physical properties of a sample of unobscured broad-line, narrow-line, and lineless active galactic nuclei (AGNs). We avoid the systematic errors plaguing previous studies of AGN accretion rate by using accurate accretion luminosities (L_int) from well-sampled multiwavelength SEDs from the Cosmic Evolution Survey (COSMOS), and accurate black hole masses derived from virial scaling relations (for broad-line AGNs) or host-AGN relations (for narrow-line and lineless AGNs). In general, broad emission lines are present only at the highest accretion rates (L_int/L_Edd > 0.01), and these rapidly accreting AGNs are observed as broad-line AGNs or possibly as obscured narrow-line AGNs. Narrow-line and lineless AGNs at lower specific accretion rates (L_int/L_Edd 0.01 broad-line AGNs, since the unbound nature of the RIAF means it is easier to form a radio outflow. The IR torus signature also tends to become weaker or disappear from L_int/L_Edd