Bins, drawers, and boxes.
Basically separated into cabinet parts, backbox parts, and playfield parts. Then assemblies are grouped together, like flipper mechs, stand up targets, drop targets, ball shooter parts, chime parts, electrical (fuse holders, battery holders, EMI filters), etc.
Then I have bins of smaller parts, such as resistors, caps, connectors/pins/header pins, fuses, and LEDs.
And drawers for various components, such as chips, transistors, diodes, etc.
I also try not to store stuff more than 1 layer deep (although sometimes it's 2 layers deep). Otherwise, if it's not visible and you have boxes and parts hiding behind other boxes & parts, you can eventually forget that you have something.