The LIS3DH is a very popular low power triple-axis accelerometer. It's low-cost, but has just about every 'extra' you'd want in an accelerometer:
Three axis sensing, 10-bit precision
±2g/±4g/±8g/±16g selectable scaling
Both I2C (2 possible addresses) and SPI interface options
Interrupt output
Multiple data rate options 1 Hz to 5Khz
As low as 2uA current draw (just the chip itself, not including any supporting circuitry)
Tap, Double-tap, orientation & freefall detection
3 additional ADC inputs you can read over I2C
This sensor communicates over I2C or SPI (our library code supports both) so you can share it with a bunch of other sensors on the same I2C bus. There's an address selection pin so you can have two accelerometers share an I2C bus.
To get you going fast, Adafruit spun up a breakout board for this little guy. Since it's a 3V sensor, they add a low-dropout 3.3V regulator and level shifting circuitry on board. That means its perfectly safe for use with 3V or 5V power and logic. It's fully assembled and tested. Comes with a bit of 0.1" standard header in case you want to use it with a breadboard or perfboard. Two 2.5mm (0.1") mounting holes for easy attachment.
Check out the tutorial for all sorts of details, including pinouts, assembly, wiring, and more!
TECHNICAL DETAILS
LIS3DH Datasheet
LIS3DH App note
Schematic
Dimensions: 20.62mm x 20.32mm x 2.6mm / 0.8" x 0.8" x 0.1"
Weight: 1.5g