I have some PSX games which I am trying to dump, but I can't get them to match the DB. I have dumped them with different drives and I am getting different results each time. The size always matches, but the checksum is different each time.
IsoBuster never reported any read errors, but all the discs have lots and lots of small scratches. I have never dumped PSX games before, so is it possible I am doing something wrong? Do I have bad drives? Or are the discs just too scratched?

Yea, if you keep getting different hashes, then that means either the disc is scratched, the drive has a weak laser, or a mix of both.  That's why it's so important to dump more than once to make sure you get a consistent set of hashes, and it's preferred if you could dump in more than 1 drive as well.

I have already tried 2 different drives, I am going to try it with another drive when I find it.
Someone gave me these games and all of them are badly scratched, but some are not yet in the DB so I hope I can find a way to dump them correctly.

Why not polish the surface using a car polishment or alike? I managed to repair a lot of damaged CDs with this method.

You can repair the scratches in the bottom side using a polishment (Rub from the centre to the edge of disc, never radially), except if reflective layer is damaged (Label side). Remove polishment´s leftovers using alcohol and dry the CD.

Moreover, you can try a Lite-On or TSST drive (With Mediatek chipset, +6 in AccurateRip´s list). In my experience, they can read flawlessly damaged discs that other drives cannot read.

On semi-vacation. MSF/AMSF to LBA/offset and viceversa calculator: link
To write properly occidental characters contained in japanese titles: screenshot
Spaces must be the fullwidth variant: link / screenshot

Agreed about the LiteOn, mine can read damaged discs that my Plextors cannot and the hashes match db.

Plextor PX-760A 1.07 (+30) : Plextor PX-716SA 1.11 (+30) : Plextor PX-W5224A 1.04 (+30) : Plextor PX-W4824 1.07 (+30) : Plextor PX-W4012TA 1.07 (+98) : Plextor PX-W1610TA (+99) : Plextor PX-W1210TA 1.10 (+99) : Lite-On LTR-48246S (+6) : Lite-On LTR-52246S (+6) : Lite-On LH-20A1H LL0DN (+6) : BenQ DW1655 BCIB (+618) : ASUS DRW-2014L1 1.02 (+6) : Yamaha CRW-F1 (+733) : Optiarc SA-7290H5 1H44 (+48) : ASUS BW-16D1HT 3.02 (+6)