I am -- by no means -- alone in this challenge. And there are lots and lots of options available.

My first purchase was one of these plastic drawer cabinets.

Pros: 

- compact
- lots of compartments

Cons:

- easy to knock over (all it takes is having to sort a pile resistors by their band colors or screws by their length and you'll be tossing this design in the trash)
- limited drawer sizes (either too small and can't fit parts or too large and results in wasted space, even with drawer separators)

Cost varies from $20 to $50 per unit. Per row/tray seems to be ~$6. With a cost of $0.50 per compartment.