Does completely unplugging your computer from the outlet save a lot more energy?

It depends - unplugging ensures that a device is completely unpowered, regardless of standby modes or possible defective switches. Some things are fully off when switched, but a computer switched off from the front panel will usually have standby power activated. It may be easier to unplug than reach around the back to use the power supply switch. Equally, most LCD TVs tend to hide the main power switch in an awkward location.

I've always heard that 5% of a monthly energy bill is due to simply having appliances plugged in continuously, whether they're in use or not. It would probably save a little energy I imagine.

Not much. But if you unpluged everything when not in use it could make a diference. Most things don't have a on/off switch. They have a on and waiting to turn on switch.

It probably will save some energy, I would do it just to be sure, and I do.