There's no hard data either way. Do what suits you best. If you're worried about a few bucks extra in power each month, or you live in an area that charges 5 times as much as others, then you might want to turn it off. If the fans are loud and it's right by your bed, turn it off. If you don't like waiting for a bootup, leave it on. In many cases, using standby or hibernation is a good idea since it means not having to wait for a bootup. The only time that you wouldn't use it is if you have some application constantly using the network or something like that.
All your hardware has a mean time between failure (MTBF) rating. If it's active continuously, on average that part will fail after that time. However most of your system isn't active constantly. Hard drives can be set to spin down (and are designed to last years even just idling, which is what they mostly do on most systems; as confused mentioned, the on/off cycles, meaning spin up/down, is how drive life is measured -- whether to let them spin down or not depends on whether the power savings and lifetime extension would be greater from allowing it to idle or allowing spindown, which would depend on how often it would be starting up). Integrated circuits (chips) and other solid state parts have lifespans measured in decades. All the terms thrown around like electron migration refer to effects that are taken into account during design. They won't likely cause premature failure just due to the system being powered on all the time. Most every effect that's used as a scare tactic to stop overclocking is actually just an effect that happens normally, but is somewhat accelerated by higher voltages and frequencies, and would eventually cause failure even in non-overclocked systems.
There are some who think that turning computers on and off can cause mechanical failure due to expansion and contraction of parts from heat. Again, no hard data to prove this affects the average lifespan of a computer. It's not likely that you'll be using the same machine by the time anything like that causes damage to the point of failure or reduction in performance.