One of the biggest complaints I get about Terraria is the hellish nightmare that is Inventory Management.
As you can see from the screenshot, I've made a few changes that should help out quite a bit. The first thing you'll probably notice is the different colored inventory windows. This is something that has been suggested a lot. (Exact color scheme subject to change.) This will allow you to more easily recognize the different item areas on the screen.
There is also a new trash can "slot." This will allow you to retrieve the last item that you have thrown away. You can also store a 41st item here in case of emergencies, just make sure to put it back in your inventory before leaving the game.
When looking inside a chest or your piggy bank, there are two new options: Loot All, and Quick Stack. Loot All is pretty self explanatory, but the Quick Stack option should make hording all your goodies a much easier task. This will look through every item in your inventory that can be stacked with an item in your chests, and place it there. The idea is that after returning from an expedition you can simply run past all your chests and click the button to quickly store all your new items, while keeping them organized the same way.
Lastly, albeit a small change, items that are picked up will now be added to your inventory from the bottom right, instead of the top left. This should help to keep your personal inventories a bit cleaner by allowing you to keep the items you always carry with you on the top, and items that need to be sorted through and sold/stored/trashed in the bottom.