Computers have multiple failure modes. Capacitors dry out or leak. Hard disks have finite spindle-bearing life. Both of those can be mitigated by removing power when the equipment isn't in use. Hard power-on processes (almost nothing has voltages that "fade up" when you turn on the switch, unless you use a variable auto-transformer, a.k.a. Variac) apply considerable stress to all kinds of elecrronic components. Anything made in compliance with the RoHS [Reduction of Hazardous Substances] laws will eventually get unreliable solder joints, especially due to thermal cycling, because there's little to no lead in the solder anymore.
A good rule of thumb might be to leave electronics/computers running if you plan to use them again within the next 12-18 hours; shut them off if you won't be using them for 2 days or more, e.g., your office computer stays up overnight but gets shut down for the weekend. In between is a gray area, and the tradeoff depends on how expensive electricity or environmental control might be versus the cost of replacing the hardware, or how much you value convenience over long lifetimes.
Not a definitive answer, sorry. -- m.