In hybrid cars, whether using NiMH or Li ion or LeFePO4, the charging/discharging algorithm is quite complex, but as a general rule, to get the longest life out of the batteries they are virtually never fully charged or discharged. If you go to some manufacturers sites you will see data that show dramatically longer life for the batteries if they are kept in the 20%-80% charge range. I can't swear that it isn't a good idea to fully charge or discharge a battery sometimes (although I am fairly certain that for lead acid/SLA/gel cell/AGM batteries, it is never a good idea to run them all the way down), but for long life you definitely do not want to regularly fully discharge (down to the shutoff voltage for lithium types) your batteries.
As to removing batteries from devices that are plugged in. Like so many tings in engineering, the answer is complicated. Depending on exactly what type of battery and what type of charging circuit and algorithm that was used, it is possible that the battery could be somewhat overcharged if left in the device. A properly implemented lithium ion battery charger should not ever overcharge the battery but some very cheap charging systems don't absolutely cut off, and some do not balance the cells well, so the battery could be hurt if left charging continuously. Several lead acid battery powered devices that I have (including my Irobot Roomba, and some big flashlights) definitely overcharge the battery if left plugged in all the time. My Roomba will actually get the battery quite hot if it is left in the dock for several days without running a cleaning cycle. The Roomba will actually wear out the battery faster if it is not used for cleaning, than if it is run every day.