My common breadboarding parts are organized in small sliding drawers with dividers, sorted by powers of 10. Resistors under 100 ohms, 100-999, 1k-9.9k, etc. Same for capacitors (no distinction between ceramic, film, electrolytic, etc., but if you have a lot, that might be beneficial). Transistors, general purpose NPN, PNP, FET (JFET/MOS, N/P), power NPN, PNP, MOS; diodes plain, zener; assorted ICs; transducers (LEDs, photocells, neon lights, piezo, etc.); fuses; jumper wires.
That's just the smaller thingy; a larger one hold bigger components (power transistors and diodes, small heatsinks, larger film and electrolytic capacitors, trimmers and pots, inductors, magnetic cores, etc.).
Bigger parts are tossed in various boxes (larger electrolytics, high voltage; low voltage; transformers; etc.).
If you have a lot of parts and a lot of drawers, you could go for finer divisions (resistors 1-2.2k, 2.3-4k, 4.1-6k, ...), or individual compartments for each value.
I haven't organized my SMT baggies yet, but when I get around to it, those will be filed upright in boxes in a similar order (by value, by family, and so on).
Tim