I saw a NOTAM about a VOR being unmonitored. I think this means that the voice capability of the VOR frequency is not in operation/nobody is listening. Is that right? If so, it just seems like something nice to know but doesn't affect the navigational capability of the VOR, right? If a VOR is unmonitored can I still use it for navigation, such as for a VOR/DME approach?
Actually it doesn't have anything to do with voice capabilities:
5-3-5. UNMONITORED NAVAIDs
a. All VOR, VORTAC, and ILS equipment in the NAS have automatic monitoring and shutdown features in the event of malfunction. Unmonitored, as used in this order, means that the personnel responsible for monitoring the facility have lost aural and visual monitoring capabilities and cannot observe the status of the facility. It does not refer to the automatic monitoring feature.
b. When a navigational aid's operational status cannot be monitored at the controlling or monitoring facility, but all indications or reports are the facility is operating normally, issue a NOTAM placing the aid in an unmonitored status.
c. When issuing a NOTAM describing a facility as unmonitored, do not use the category of monitor, only the contraction UNMON.
!DCA LDN NAV VOR UNMON
(Source: JO 7930.2M)
So basically it says that this VOR may malfunction without notifying a responsible party, or that a responsible party is no longer monitoring the VOR. A lot of times this is done with VOR's that are scheduled to be removed from service, they may be allowed to continue to operate but are no longer maintained.
You can still use the VOR for navigational purposes. The VOR is supposed to shut down in the event that it becomes unusable, so you can be (relatively) assured that if the VOR is operating, it is reliable and usable.