Is there a shortcut to move items between your inventory and the crafting table?

Items can be moved rapidly from your hotbar to the crafting table quickly by pressing the corresponding number while hovering your cursor over the desired destination slot in the crafting grid.

This is most useful when crafting a lot of something that takes only one ingredient.

1. craft a few of the destination items the "slow" way and use those items to reserve slots for that item in your inventory. At this point your inventory should be totally full, with some of the ingredient in slots 1 and 2 of your hotbar.
2. Arrange for a large amount of the ingredient to be on the ground at your feet. This can be done by breaking a chest full of only the ingredient.
3. open the crafting grid, move your cursor to the desired slot in the grid and press 1 and 2 to move the items into the grid. As you do this, more items will be picked up off the ground to replace them.
4. Shift click the crafted item into your inventory into the slots you reserved for it in step 1.
5. repeat steps 3 and 4 until no more items are on the ground.

Here's a video by jl2579 demonstrating the technique

There is a way to quickly move items into the crafting table.
As TokenMacGuy said, you can do this by hovering your mouse over the slot in the crafting table and pressing the corresponding number for the one in your hotbar.

Here's list of controls to quickly move around items in your inventory that I know of:

Double Left Click - sort loose items into one stack.
Hold and Drag Left Click - split a stack evenly into each inventory slot.
Hold and Drag Right Click - place one item from a stack into each inventory slot.
Shift + Left Click - move all the items from the stack into the hotbar/out of the hotbar. Put items in/out of chests, furnaces, enchanting tables, anvils, brewing stands, beacons, dispensers, droppers and hoppers. It will also put on and take off armour.
num 1-9 - if you hold your mouse over an item and press a number it will put that item into the number in the hotbar.

EDIT: Turns out there is a way to move items into the crafting table but I will leave this answer. Found out how to do those keyboard things.