I had this problem as well. I never used screen lock. I updated to Kit Kat (which I hate). Then a while later, I turned on screen lock temporarily. When I attempted to turn screen lock off again, I was unable to select the "None" option.
I tried the No Lock app suggested by Whitney Ingram above, which mostly works, but it froze my Nexus 5 several times in a span of two days, forcing a reboot each time.
Finally, as Adryan Adrian suggested above, I tried removing the security credentials via Settings/Security/Clear credentials and then the "None" option for screen lock was enabled again. I don't know exactly what credentials it cleared, but so far it didn't break anything.