HC-SR04 Ultrasonic sensors can measure distances fairly accurately and are very useful in many Arduino projects. I've used them in autonomous robots, electronic instruments, and many other projects. They have a range of 2 cm - 400 cm (~ 0.8 inches - 13 feet) and work best against flat surfaces.
Step 1: Video
This video should help explain how to use an ultrasonic sensor.
If you have any questions leave a comment here or on the video and I'll help you as soon as possible!