I have seen the Enderman pick up grass blocks but I want to know is what blocks they can pick up and what block they can't pick up.
As of Minecraft 1.8.1, Endermen can pick up and any solid, entirely cubic block except the following:
- Any double slab
- 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:
- 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 is no longer possible. They cannot pick up water or lava.
Using Minecraft Coder Pack (MCP) to decompile Minecraft and deobfuscate its source code, as of 1.3.2, the following are the only things Endermen are allowed to pick up:
- Flowers (red and yellow)
- Mushrooms (brown and red)
Endermen from what I've seen and heard can pick up most types of blocks including natural and player-placed blocks, chests, furnaces, noteblocks, mob spawners, obsidian, and bedrock. There appear to be some types that they cannot pick up, but there is not yet any final list of these.
A user on the Minecraft forums gives an account of an Enderman picking up his chest, causing the items to burst out everywhere (as I commented extensively on Sir_Tiffy's Reddit thread, chests cannot be moved with their contents intact for the same reasons pistons cannot push them).
I'd post more links but the spam prevention won't let me since I don't have any rep yet.
Enderman can pick up any full block, except obsidian. They cannot pick up transparent blocks such as glass, glass panes, stairs, half-slabs, etc.
Enderman can pick up simple items like dirt, stone, brick, ores, ect. I have seen them carrying flowers, but they are mostly spotted with dirt or, when in caves, stone. They can not pick up obsidion or bedrock, and they do get mad at blocks that they can not pick up. Clearly, enderman are the smartest mobs , and can actually outsmart steve. they can see up to 64 blocks away.