Is it better to leave an electronic device on or to turn it on and off?

It depends on the device, power consumption and physical environment.

Computer equipment: Generally happier when left powered on with the exception of the hard drive and monitor (both of which have sleep modes available). The hard drive has moving parts that will eventually wear out if left running for prolonged periods. The solid state components have delicate soldering points that are prone to cracking if heated and cooled repeatedly.

Televisions: Tube televisions are best left off when not being watched. It saves power and causes less wear to the phosphorous coating in the tube. LCD TV's are best put to standby mode. Plasma screen TV's are MUCH better off when turned off -- the plasma screens have about a 7-year lifespan under normal conditions, and are very expensive.

Misc: Older electronics using vacuum tubes are way better off left on for less wear on the components, but will suck a lot of power. Anything with moving parts is best turned off such as DVD players, XBox consoles, or anything that reads moving media.

Environment: Humidity is an electronic nightmare. Leaving the component running will help to fend off the ravages of moisture, but make sure to clean any exposed vents regularly with compressed air. Vibration is very bad for electronics in an on state. If you live near railroad tracks or on a ship, electronics will be better off if you turn them off while not using them. This is especially true for high-heat components such as amplifiers, televisions, and computers.

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Another concern is that many audiophiles feel that audio equipment, especially an amplifier, does not sound its best until it has come to a stable, warm operating temperature. That can take an hour or more.