It seems that a gyroscope sensor is currently not so common amongst Android devices. But does an accelerometer (in conjunction with the compass?) provide enough accuracy to measure angles (tilt, yaw) with high precision?
Sufficiently for what, how high a precision?
There are a number of apps that will measure levels and angles purely using the accelerometer, that are good enough for everyday use, after an initial calibration.
For examples see the range of Spirit Level apps available on the Market.
If you're interested in sensors, you might want to watch this Google Tech Talk - Sensor Fusion by David Sachs.
Accelerometer provides an approximation of angles, but it does not provide a good accuracy. It has a major fault in that it amplifies hand jitters. That can be fixed with a low-pass filter, but that will introduce a delay when there is actual change in angle (which could cause a visible problem in reactive games and sensor log).
However, Gyroscope is not the king of measuring angles either. Gyroscope has a major flaw in that its measurement have a long-term drift. Therefore, accelerometer and compass will need to be used to correct a gyroscope.