The Arduino boards provide an analog input range of 0V to 5V which translates to 0 to 1023 integer values. The range is determined by the on-board ADC, which in the case of the Uno is a 10 bit ADC (2^10 = 1024).
Do any of the official boards have a larger (>10 bits) ADC? Do any boards provide a wider range of analog input values?
AVR-based Arduinos only have 10-bit ADCs, but the ATSAM3X in the Due has 12-bit ADCs. Additionally, it is possible to interface to higher-resolution external ADCs via I2C or SPI.
How much accuracy do you really need? If it's just 1 or 2 extra bits of resolution you are after, you might be able to achieve that with a bit of oversampling.
Basically, you take a ton of readings and average them. It only works if there is at least a few mV of random noise in your signal or in your ADC, and if your input signal bandwidth is low enough to be averaging samples together.
Otherwise, go with a dedicated ADC chip.
They all do with oversampling. You can evaluate the quality of doing this for your own use.
