Bear in mind that while what he said is correct, there are other concerns on an assembled board, as opposed to the bare chip. Arduino has a voltage regulator that is always consuming current. The Power LED is always consuming current. You should be sure to set pin 13 (the indicator LED) as an output and turn it off, since even as an input, there will be leakage current through the LED. The other active components on the board have their own quiescent current levels, etc.

You can get an AVR device to run on a coin cell for months or years (I have a design that does just that). You'd have to modify an Arduino significantly to do the same.

Very true, though there are some better Arduino variants. The Pro mini is the canonical "low power" Arduino as it uses a very efficient LDO regulator. I also use bare ATTiny's for a lot of uses, they don't require any passives and can run directly from a LiPo as long as you use a protected cell or connect a feedback line to the ADC.