In the past year there have been plenty of changes, I'll try to list them in chronological order over the past year and by only focusing on the additions to the game (I'll also try to mention where possible what my explanation is if it's not so obvious):
Minecraft Beta 1.0 - December 20th 2010
- Throwing an egg has the chance to spawn a chicken.
- Inventory tooltips when you hover over an item.
Minecraft Beta 1.2 - January 13 2011
- Charcoal added to the game (This is smelting wood in a furnace as an alternative to mining coal ore)
- Note blocks (This is a special type of block that allows you to play a musical note depending on what type of block it sits on top of)
- 15 wool dyes (You can now "dye" a sheep for extra wool of a different colour, or use the item to dye wool already in your inventory. See this list of dyes).
- New passive NPC, the squid. This drops an ink sac.
- Different types of tree (birch & pine)
- Reeds are now sugarcanes.
- Can now create cake.
- Extra crafting recipes.
- Bones can be made into bonemeal (This is used to make things grow faster, e.g. trees)
- Sandstone exists (Basically sand but a stone variety that can be mined)
- Dispenser blocks introduced (Basically put arrows in them to create a trap with redstone).
Minecraft Beta 1.3 - February 22, 2011
- Beds can now be made (Sleep at night time to advance time, but this doesn't accelerate crafting time - in a later patch the bed will also reset your spawn position so if you die you start there).
- Half size blocks now exist (Useful for steps!)
Minecraft Beta 1.4 - March 31, 2011
- Wolves are now in the game. You can tame them and they'll follow you around, or you can kill them.
- You can now craft cookies!
- If you sneak on a ladder you hang onto it.
Minecraft Beta 1.5 - April 19, 2011
- Weather added to the game (Rain, snow, etc).
- Achievements are now in the game.
- New blocks (Mainly rail related ones for carts such as powered lines and dectetors)
Minecraft Beta 1.6 - May 26, 2011
- The nether finally works in multiplayer.
- Maps can now be crafted (Basically they show you a map of the area as you walk around you create the map).
- Trapdoors added.
- Record player can now support more discs (Discs added later)
Minecraft Beta 1.7 - June 30, 2011
- Pistons added to game (You can push blocks along basically)
- Flint and Steel or redstone is the only way to make TNT blow up now.
- Shears were added and now required to get wool off a sheep or pick up leaves.
Minecraft Beta 1.8 (Adventure update) - September 14, 2011
- New mobs (Enderman, Silverfish and cave spiders)
- New blocks (A lot to list! See reference at end)
- Creative game mode added.
- Terrain generator which will now allow you to generate towns, strongholds, abandoned mine shafts and ravines.
- Food system introduced (You now need to eat to stay alive).
- Sprinting added to the game.
Minecraft 1.0.0 - November 18, 2011
- New nether blocks and now a Nether fortress.
- "The End" (unofficially called "The Ender", or "Enderlands"), which replaces the previously announced Sky Dimension.
- There is now an end portal to take players to the end to fight the enderdragon (new mob).
- Endgame/Credit screen (You can still play your world)
- New stones from the End world to be found.
- Mushroom biomes and mushroom cows!
- You can now gain experience for enchantments and for score.
- You can now breed your own animals (feed them and put them together).
- Breeding causes baby animals :).
- There are now unlimited strongolds per map (it used to be three).
- Enchantment table added to make potions and also the enchanting skill (put specific items together and pop, here's your potion!).
Here's the reference I was using to type this up.