Yet another long winded and somewhat technical explaination if you are really interested:
Regarding P=VI, it doesn't fully hold at AC, like RetroACTIVE mentioned. There's the possibility that the current and voltage may not line up exactly with each other in time, and then you have to account for that loss of power. Your meter reads RMS voltage and RMS current, which doesn't account for that. For devices using SMPSes ("switchers"), you have to assume a power factor of something like 0.6-0.9. It can be higher or lower depending on the design of the supply and how heavily it is loaded. Linear supplies can vary from very good to very poor power factor, depending on design (I've seen <0.3 before). Then P=VIcos(phi) where cos(phi) is the power factor (V is RMS voltage and I is RMS current). Complicated explaination I know, but the math is at least fairly simple in the end.
If you just multiply RMS voltage times RMS current, you get "apparent power" (in VA) which is also a useful number as that's how you have to rate transformers. For sizing circuits (breaker and wire size), you just need to know the expected RMS current. Note that on devices with SMPSes, current will increase as voltage drops so that it draws about the same amount of power.
Note that the power company bills residential customers based on kWh, so actual energy (power consumed over time) and doesn't consider power factor. Industrial and some commercial customers are penalized for having poor power factor since it costs the electric company money. All that extra juice (the difference between apparent and actual power) results in current "sloshing around" in their distribution network heating up wires and going to waste. There are ways that large customers can correct this if the penalties are high enough to justify it, but for residential customers it isn't really a concern.
This is useful information, though. As a note, the inrush current on some devices can be several times their rated or steady-state draw, not just double. My upright cabinet's monitor's rating for inrush current is 30A! Turning on my Pump It Up machine causes the lights to briefly dim and UPSs on the same circuit to drop the utility line momentarily. These inrushes are very short lived (and hence aren't dangerous from a wire heating perspective and won't cause breakers to trip in most normally loaded cases), but are something to be aware of.