I have a power/watt meter handy, so I thought I'd measure the family PC in various modes. It's an old 1.8 GHz AMD Sempron eMachine. This is just the box, and not the monitor or any other peripherals.
- Off (just plugged in): 3.0 W
- Stand-by (everything off, LED flashing): 4.5 W
- On, but idle: 75 W
Like all device that don't use a hard, physical switch (TVs, DVRs, etc.), you will get some power draw on the order of 1-to-5 watts per device. The costs of these "ghost loads" over a year depends entirely on how many you have and what your kW-hr billing rate is.
Being a power miser, I use a power strip on the family PC, attach everything to it, and then flip the main switch off when not in use.
EDIT: I did the math for this machine while "off". My rate is 8-cents per kWh, so:
3W * (1kW / 1000W) * (24h * 365) * $0.08/kWh = $2.10
This is an absolute lower bound on the cost of having the machine plugged in for a year. With typical use it will be much more.