What
hawhill suggested can find a "totally dead" battery.
But in many cases, voltage measurement alone is not enough. A battery needs to be tested under load over a time period to determine its remaining useful capacity. Lithium batteries are considered "dead" when their remaining mAh capacity is too small to be useful. The portion of lithium in the battery that no longer holds a charge is called its "rock content". A battery that is almost entirely "rock" still can show full voltage, but it will disharge quickly under load. Lithium battery chargers usually refuse to even charge a battery that is beyond its useful life, to prevent even a minimal risk of fire
For more info, here is a good place to start:
http://batteryuniversity.com/learn/a..._ion_batteries
According to this, most "portable device" batteries are only good for 300 to 500 charge/discharge cycles:
http://batteryuniversity.com/learn/a...e_battery_life