I read that an ILS is a precision approach system. It provides a final approach with precision in both horizontal and vertical guidance to the runways. But I don't know how precise it is because there were a number of accidents related to landing operations.
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.
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.
ILS is can be very precise, but there are many factors that may compromise the precision. When all these factors are avoided, automatic landing with no visibility is reliably possible.
The ILS installations are classified in three categories:
CAT I: Category 1 allows for decision height (DH) no less than 200 ft (height, so above ground level).
ILS creates the signal by interference of different signals emitted by offset antennas. If one of them fails, but not the other, the signal may appear as perfectly centred to the instrument on board of the approaching aircraft with no way to tell that it does not actually work. Therefore pilots should cross-reference their position using other sources (DME, VOR, ADF, marker beacons).
There is a video about this kind of failure (describes an actual incident where the glide slope stopped working without indication, the crew noticed by cross-checking against DME and altitude, plus description of the failure), but I can't find it now.
CAT II: Category 2 allows for DH not less than 100 ft and allows using auto-land until touch-down. It needs to have far field monitoring that can detect incorrect or incomplete signal and the transmission system has to be doubled. It also needs to be somewhat more precisely aligned than CAT I.
CAT III: Category 3 allows auto-land including roll-out. It has subcategories IIIa that allows DH not less than 50 ft, IIIb that allows DH down to 0 ft (so effectively no DH) and visibility 75 m (otherwise the plane could not taxi off the runway as there is no guidance for taxiing; when there is, it will be called CAT IIIc). It has stricter limits on precision and monitoring than the CAT II.
Independent of the category, direct line of sight is needed. The signal is not affected by fog and precipitation, but is distorted by any obstacles. Aircraft or even small vehicle crossing the runway or taxiing in front of the transmitter will significantly distort the signal.
That's why each ILS CAT II and CAT III installation has ILS protected areas and to actually use auto-landing, special procedures need to be in effect that keep these areas clear. When they are not, incidents like Singapore B773 at Munich on Nov 3rd 2011, runway excursion happen.
Similarly attempting to auto-land on CAT I lead to accidents like Air India A320 at Jaipur on Jan 5th 2014, runway excursion on emergency landing.
"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."
I know of at least one reader who has a problem with this statement, so I'm only adding these comments for clarification. EGID is correct. Think of the localizer as a funnel ... the "hopper" end of the funnel catches more liquid when it is bigger and fans out wider ... but it ultimately leads to the same narrow downspout. If the purpose of this funnel is to catch and direct more incoming liquid (aircraft) then it's doing no one favors to have too narrow of a hopper. All funnels are very precise on the small end. You want an ILS to be fairly forgiving for the reason that you may be intercepting it while blind and in the soup.