The X-ray transient XTE J1701–462 was the first source observed to evolve through all known subclasses of low-magnetic-field neutron star low-mass X-ray binaries (NS-LMXBs), as a result of large changes in its mass accretion rate. To investigate to what extent similar evolution is seen in other NS-LMXBs we have performed a detailed study of the color–color and hardness–intensity diagrams (CDs and HIDs) of Cyg X-2, Cir X-1, and GX 13+1—three luminous X-ray binaries, containing weakly magnetized neutron stars, known to exhibit strong secular changes in their CD/HID tracks. Using the full set of Rossi X-ray Timing Explorer Proportional Counter Array data collected for the sources over the 16 year duration of the mission, we show that Cyg X-2 and Cir X-1 display CD/HID evolution with close similarities to XTE J1701–462. Although GX 13+1 shows behavior that is in some ways unique, it also exhibits similarities to XTE J1701–462, and we conclude that its overall CD/HID properties strongly indicate that it should be classified as a Z source, rather than as an atoll source. We conjecture that the secular evolution of Cyg X-2, Cir X-1, and GX 13+1—illustrated by sequences of CD/HID tracks we construct—arises from changes in the mass accretion rate. Our results strengthen previous suggestions that within single sources Cyg-like Z source behavior takes place at higher luminosities and mass accretion rates than Sco-like Z behavior, and lend support to the notion that the mass accretion rate is the primary physical parameter distinguishing the various NS-LMXB subclasses.