I was thinking about a way in which you could tame animals, and here's what I came up with. I read a few similar threads like this one but I've come up with a different solution that I think works better (sorry).
These next few sections show how you make an animal yours, tame it, get it to a location, and then what happens.
Make A Brand:
First off, you need a way to tame animals. In order to do this you give them a brand. How do you give them a brand? First you make a branding iron.
  
Heat The Brand:
This turns into a simple stick with a piece of iron on it. This will serve as the base of our branding iron. Now in order to take an animal, you need to heat the brand. To do this you stick it in the furnace. The brand will stay heated longer depending on what you use to heat it with, and it will give you a hot brand when it is done, the brand looks very similar to the regular one except that the tip is now glowing.
Wood: ~2-5 Minutes
Coal: ~15 - 30 Minutes (Multiple coal doesn't make it work longer as it wouldn't burn any hotter, just longer)
Bucket Lava: Will it ever cool?
Now, once your brand is hot, you need to find animals. The way this works is very simple. You "attack" the animal with the brand which will hit it, and add a new mark to the skin. The mark is similar to the old skin except that it has a round / square circle on its hind quarters. That animal is now yours.
Now while you have the brand out, you can "use" the animal. If you use it, the animal will begin to follow you. When you use the animal again, it will stop following you. This is what allows you to tame an animal, and then bring it to a location (probably a pen, or maybe make it drop off a cliff with you).
After an animal is branded, it will not despawn. All other animals that are not branded, will continue to despawn. In that way, the issues before are addressed where you can take the animal to a pen, it will be contained by the fence or however you have built it, and you know that when you come back later it will still be there, however, animals that randomly spawn inside your fence will later despawn (unless you brand them before that).
Once you have a tamed animal, you may want to ride it around and bring it places. In order to do that you need a way in which it can be kept in a very limited area. The reason for this is that while it is yours, that doesn't mean you want it to be either following you or wandering aimlessly, who likes finding their pigs in the morning after a hard day in the mine. To make an animal yours you first need a collar.
To make a collar: (Sorry I can't find wool from a sheep, but you get the idea).
 [wool] 
[Wool]  [Wool]
 [wool] 
Alternatively to make it harder, you could have to spin the wool first into thread, or reads into rope, and then use four of them to make a collar.
The collar on its own does nothing, in order to make use of it you need to attach it to a leash. In order to do that, you add some extra rope to the side of it.
 [Collar] 
 [Rope] 
 [Rope] 
This now gives you a collar with some line attached to it that can be used on your animal. Use the animal with it out and it will put the collar on the animal, It will then show you holding the leash. Click a block around the animal and it will secure the leash to that spot. The block it spawns on the ground looks like a stake in the ground with the animal attached to it. The animal will now be unable to wander more than a spot or two from that spot .
To remove the leash, hit the stake it creates in the ground and it will despawn like a candle, and can be picked up again for later use.
Overall this is the sum of the idea. It could be used on cows, pigs, chickens? It would be very nice if they ever add horses to the game as well as I'm sure people will want to ride those.
This is a good idea. I don't know about the leash, you could just build a fence with a door, herd them in, go out and then close it. Or maybe when you right click them again they stop following you. But it's a good idea still.