How precise is an ILS (Instrument landing system)?
The ILS is precise enough to allow landings in essentially zero visibility, including those performed by autoland. 

The ground based bits

The vertical range is 1.4° (0.7° above glideslope, 0.7° below) and the horizontal varies, but is a maximum of 6° wide. What this means in terms of how many feet or meters off the centerline an aircraft is varies depending on where the aircraft is on the approach, but it's generally correct to say that the closer an aircraft gets to the ILS antennae, the more precise the system is.

The specifications for a localizer antenna require that it be no less precise than ±10.5m - this is for a Cat I approach, and it gets correspondingly more precise as the category increases.

There's always the risk of interference with the transmitters; as noted in the comments, accidents have been caused by airport vehicles parked in the ILS critical area, interfering with the signals, and as the equipment ages it can require recalibration.

The airborne bits

It's possible for receivers to have issues that could affect precision; antennas can get loose connections or become covered in ice, while pilots might interpret indications incorrectly, misread reverse sensing, or intercept a 'false glideslope' from above.

Regarding accidents

You're correct - there are many accidents related to landing operations. That said, you may be including those which weren't flying an ILS approach - it's hard to say since you aren't citing anything. Still, it's possible that there's confusion between navigation precision and safety of flight.

Many (not all) of landing accidents involving instrument approaches do center around human error rather than equipment failure; pilots tuning in the wrong frequency or incorrectly setting avionics and instruments (reversing the inbound course on an HSI causes reverse sensing, that sort of thing), or people on the ground screwing up.