I tend to run my "favorite" engines while the others sit on display sidings for appearance sake. Do extended periods of idle time have a deletarious or positive affect on engine life and/or performance?

A car, for example, when it sits too long in the driveway seems to devlop moans, creaks, and small operational problems. I wonder if regular operation might. in fact, be good for a 3-rail O-scale engine?

Maybe the engines that just sit and sit are the ones that will last forever?

I would think the things you have to worry about are dried lubricants, rubber tires, flat spots on rubber tires, and dead batteries.

When I was writing maintenance procedures for the Navy we had "Lay-up" and Start-up" maintenance. Lay-up maintenance included things like removing batteries, draining some fluids, covering equipment to prevent dust/dirt accumulation. Start-up maintenance would include re-charging batteries, lubricating moving points, cleaning, etc. Things like turning a piece of equipment on to make sure it still works was part of the plan at one time, then it was taken out. Turning on a light every month to make sure it works doesn't guarantee that it will work the next time, although some may argue that it enhances operator confidence.

I believe a good "start-up" procedure for an engine that has been sitting idle for long periods of time would be a good idea, maybe I'll publish a Planned Maintenance System (PMS) card for electric trains

Second thought...what do sellers (LHS, online shops, private sellers) do when someone buys an engine that has been sitting for years??? I bet most do nothing but hand it or box it and ship it to the new owner.

I think they just last longer. I pulled out my original tin plate locos last year that had been in storage, ie, not run for nearly 50 years.I cleaned the commutator and brushes, gave them an oil, and off they went. They are still like new.
What has been said about batteries and rubber tires is right but no big deal .Just make sure your trains are stored in a dry stable temp environment.

The only problem I've had with sitting trains is the foam in MPC equipment. It rots over time and messes up the electronics. All other advice is excellent.