We have plant farming and pig farming, etc. Why don't we have apiaries?
I think that on trees there should be a chance for there to be a bee hive hanging from a leaf block and you use a smoker to put the bees to sleep so you don't get stung to death. Here is the recipe for a smoker
  
The smoker would run on wood planks and they would burn up in 20 seconds. The way you use the smoker is your right click on a beehive and the bees around it would all fall to the ground, the bees would be knocked out for 30 seconds which would give you time to break the hive, take the honeycombs, and run away. Now you do have the choice of not using a smoker but that would mean having a whole beehive after you. This would be an ailment like fire and jumping into water would be the only way to get rid of them or wait 25 seconds for them to give up on you. The bees model would be a simple 3 pixels that would go like this (they would move very fast so their models wouldn't have to be complex)
When you smash the hive you would have a chance of getting 1 to 3 honeycombs. You could use these honeycombs to start an apiary or they could just be eaten raw. If you put them on the crafting table it would turn it into 3 honeycomb meals (ground up honeycombs) and you could put those in the furnace and turn it into honey.
The option of choosing an apiary would be like farming, so you would have control over the amount of honeycombs you would be getting. The success rate of an apiary would be based upon how many flowers there are in a 10 block radius of the bee box. So a lot of flowers means a lot of honeycombs , the idea is 5 flowers=1 honeycomb a day, so if there are 15 flowers around it you will be getting 3 honeycombs a day . Harvesting honey combs would be similar to getting them from trees but there would be a larger quantity of honeycombs. The way you would build a bee box would be this
(the final product is unfinished, I am still working on it, it will probably be a white box with a hexagonal beehive pattern on the top)
The interface for the bee boxes would be like an chest only you would not be able to put things in only take out honeycombs. You would not be able to take all of the honeycombs from the bee box, you would have to keep one inside at all times to keep the bees thriving. They would look like this
The stats of bees, honey, and honeycombs are up for debate, as not to make this idea too overpowered/underpowered.
Great idea - I'm not sure about the smoker, it seems a bit specialised which doesn't really fit, and I think you should be able to remove all the honeycomb. We'll just assume the "chest" area only displays the excess and the honeycomb the bees need remains integrated into the apiary.
Excellent idea, very good drawings, well thought out. I like it.
I really love this idea. Though I think getting 3 honey combs per-day per-box would be too much, then having each of those break into 3 honey comb meals would be overkill. Maybe honey combs are eatable as they are, and putting those into a furnace will make honey, just skipping the "honey comb meal" part. Honey combs in apiaries should produce constantly sort of like crops do now, but the more flowers near the apiaries the faster they'll be produced, instead of having it a per-day thing.
The bees should be a single AI entity that will move slightly slower than a player, and will look like a swarm of bees. The single bee entity will be in the hive most of the time and occasionally move towards flowers near the hive. They will be peaceful until a player attacks their hive, when that happens they'll chase the player for up to 100 blocks away before giving up, and will give up if the player goes into water. The bees will damage you every few seconds when they are close enough, sort of like the cactus.
Player built apiaries should still have the bee entity, and you'll still have to smoke the bees before obtaining the honey combs.
I Personally think you should be able to use a jar to collect bees and use them as a thrown weapon. the ancient greeks did this with scorpions and termites, why cant we have bee grenades?
OMG i love this, and it would be great for people beggin for grenades, while keeping in the spirit of minecraft. thanks for all the great suggestions guys, Looking back at it, I guess the comb meal would be a little much, but heres my take on it.
A raw honey comb would heal lets say, 4 hearts.
honey would heal 6 hearts (it would cost 3 meals to make one jar of honey)
Although you would get more health from honeys than a honey comb, it would take coal to burn the fire to power the furnace. So it would be your choice whether or not to grind it into meal and cook it into honey, depending on how much coal you have, you could choose what to make. Of course these numbers are only hypothetical, i would leave the game balancing to notch.