The AVR chips only have 10-bit ADCs. If you need a more sensitive ADC, you can get an ADC chip that will do this. These chips have well documented protocols (like SPI or I2C), and should be easy to interface with the Arduino. I recall seeing something about this on the Arduino playground or in the forums, but it should be relatively straightforward.
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No, 10 bits. See this page for more info: http://arduino.cc/en/Main/ArduinoBoardDuemilanove ("Input and Output"). I'm sure you could wire up a third-party ADC if you wanted to. There might be some other Atmega chips that can do this.