There are a couple of problems with leaving a PC on:
Power consumption: PCs consume quite a lot of power - a mid-range system could use as much as 150W excluding monitor. Leaving that base unit running 24/7 would cost me about £10/month (representing a near 40% increase in my electricity bill).
Wear: PCs contain mechanical parts such as hard-drives and fans. 'Consumer grade' hard drives such as would be found in a typical home PC are only designed for intermittant use (300 power-on hours/month is typical). Usage of such drives in a 24/7 system could shorten their life, which for consumer grade drives is often already short (3 years expected life-time - 1 year warranty). Other parts such as fans also have limited lives - this shouldn't be a problem for a Dell, but for cheaper PCs, with low-cost components, fans are prone to clogging with dust, or simply failing. Even the electronics wear out - certain components (particularly capacitors) are often running under high temperatures and electrical stresses and have a finite lifetime (10k - 20k hours)
In my opinion PCs should be switched off when not in use, or at least put into standby mode, so that the bulk of the components are powered down when not in use. You'll save energy, money and your PC will probably last longer.