What blocks can Endermen pick up and what blocks they can't?

I have seen Endermen pick up grass blocks, but I want to know what all blocks they can pick up and what blocks they can't pick up.

This is no longer relevant for the current version of Minecraft, but in Minecraft Beta 1.8.1, Endermen were able to pick up and any solid, entirely cubic block except the following:

• Any double slab
• Bedrock
• Chest
• Dispenser
• Furnace
• Jukebox
• Monster spawner
• Note block
• Piston and sticky piston
• Snow block

They can, however, pick up the following blocks which are not entirely solid cubic blocks:

• Cactus
• Flower (both types)
• Mushroom (both types)

Notably, tilled farmland is not a full height block and the Endermen cannot pick it up, but if they walk on it, turning it back into a dirt block, they can pick up that dirt block. Likewise, Endermen cannot pick up stairs (any type), half slabs (any type), fences, doors, gates, iron bars, cobwebs, beds or cake.

Endermen cannot pick up things attached to blocks, such as buttons, ladders or redstone wire. However, they can pick up the block it is attached to, which will cause the attached thing to drop as if the block was destroyed.

Endermen can pick up both naturally occurring blocks and blocks placed by players. In the Minecraft 1.8 pre-release they were able to move bedrock, but as of Minecraft 1.8.1 this was no longer possible. They cannot pick up water or lava.

(Sources: Sir_Tiffy on Reddit, MrPixelTech on Youtube, testing in Creative mode, and the swiss cheese pattern of Ender-holes in my monster grinder)

As of MineCraft 1.7.4, the following are the only things Endermen are allowed to pick up:

• Cacti
• Clay
• Dirt
• Flowers (red and yellow)
• Grass
• Podzol
• Gravel
• Melons
• Mycelium
• Mushrooms (brown and red)
• Pumpkins
• Sand
• TNT

Source: Looking at the source using Minecraft Coder Pack (MCP) for MineCraft 1.3.2, and the MineCraft wiki for later versions.