One thing nobody's said yet is Emerald Ore. You can get an infinite amount of emeralds by trading with Villagers, but the only way to get Emerald Ore is to find one in an Extreme Hills biome (and they only spawn in groups of one) and mine it with a Silk Touch pick of iron or better. Yes, the Dragon Egg is rarer, but Emerald Ore is the rarest reobtainable block.
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"Redstone is a powerful thing. By itself, it does a lot of crazy stuff. When you add lots of it together, it does even more crazier stuff." -Dinnerbone
Rarest item would be chain armor, followed up by ghast tears.
Rarest block would be the dragon egg; only one obtainable per legit world. Rarest re-obtainable block would be chiseled stone brick, followed by mycelium.
The Meaning of Life, the Universe, and Everything.
The (true) rarest blocks/items are the finite ones. NO, End portal frames are less rare than the Ender Egg. Finding difficulty only applies to rarity in infinite blocks. 36 > 1, so the Enderdragon Egg is more rare. Also, if you find a dungeon, saddles are NOT rare. They are almost always a loot item. Finding Natural Golden Apples is a dungeon rarity, however.
Also, stone is no longer the most common block. Air is. (as of 1.2)
Golden apples:2 ( you need one apple and 8 golden blocks,NOW HOW CAN YOU GET THAT,[unless you live in the nether -_-])
The following are only legitimatly gained through silk touch tools:
Monster Spawners (not sure,I haven't tested that out yet)
Has no one said Naturally Spawning Pink Sheep yet?! They have less than 1% of spawning in a sheep herd!
-Desert Wells: A 1/1000th chance of spawning in any Desert chunk. I call that rare.
-Slimes: Even with a farm set up in a Slime chunk, they seem so rare.
-Music Discs: Dungeon Chests on RARE occasions, and the challenge of lining up a skeleton and a creeper perfectly.
-Dragon Egg: One per world.
-Legit Survival Chain Armor: Blacksmiths get a small chance to offer it.
-Chiseled Stone Brick: Only 3 per Jungle Temple.
-Emerald Ore: Rarer than Diamond.
-Ghast Tears: They always seem to drop the tear in lava or fire.
Mooshrooms: Only spawn on Mushroom Islands, which are THOUSANDS of blocks from spawn.
I guess I should post, I'd say the finite blocks, only ones are mossy/cracked stone brick, end stone, and the dragon egg, Cuz theres only one end, and not a lot of end stone, one dragon egg, and 3 strongholds, so not a whole lot of the stone bricks, circle stone brick is rare as hell, but it is infinite since theres no limit to the temples, and slime balls are rare cuz of slime spawning conditions, but they can easily be farmed. So all-in-all, the finite blocks of mine craft. Also cocoa beans used to be before the farming was added.