Out of curiosity are the ones that won't load all a particular type or are all your games the same (all silver bottom)? If it's one particular type it is probably due to a lens being misaligned or dirty. You may also want to check the discs that don't work for scratches or dirt.
The other possibility is the PS2 may be on its dying days- if cleaning the discs or the lens doesn't help you may need to contact Sony's tech support and see what they recommend.