Back when my dice collection was smaller, I used to keep my dice in a large aspirin bottle (with child-proof lid). Now I have two normal-sized dice bags, one for polyhedrals, one for d6s (we used to play a lot of Champions).
We also use a deck of playing cards every D&D session. They work great for intiative: assign every enemy a specific card (three goblins? - ace, two, and three of clubs; BBEG? - King of spades) and then mix in the PCs' homemade cards with their pictures on them (cut to playing card shape from an index card and covered with Contact paper after their drawing is finished with colored pencil). After a character takes his/her turn, the card goes to the bottom of the initiative stack.
We use Lego people for PC miniatures and assorted game pieces for just about everything else. (I bought up a bunch of "generic" game pieces from a dice company at Gen Con.) I use old check boxes to store game pieces in.
Johnathan