I am going through some basic electrical stuff in a house that had some pro and some amateur work done. Some of the things I've been working on (e.g. light switches) have been wired correctly (breaking the hot wire only) but the ground wire was simply cut short at the romex and remained unused. I assume this was done because the switch had no ground screw. However, it seems to me that the ground should remain intact--maybe wire-nutted to the other ground wire(s). Your thoughts? Thank you.
If you have a metal box then it should be grounded. That has been in the NEC forever. Since 2008 or 2011 (can't remember) light switches have been required to be grounded but if your house was built before that then you are not required to bring it up to code. It is grandfathered, otherwise all homeowners would have to make changes every time the code changes.
However, it is never a bad thing to bring things up to current code if you want. And yes if you have multiple ground wires in a box they should all be connected together.
At a light switch, it is likely that the ground wire is a spur, i.e. it is only there to ground the light switch should the light switch need it. If it's a light switch that doesn't need grounding, then the wire end should simply be terminated. In the UK that'd be in a connector block, in the US I believe a wire nut is more common.
(If there were two ground wires in the switch box, then they may need connecting for ground continuity. But if there's only one, then it's a spur, and hence no continuity needed.)
Should you take and replace the switches, then purchase switches with ground screws. If you have a plastic j-box then you should try to splice the bare wire and connect it to the switch.