Antagonists should be someone or something (e.g. a natural disaster) that presents a difficult challenge for the main character, and at times, this challenge may be seemingly impossible to overcome. The key here is that the antagonist doesn't necessarily have to be evil, they just need to present problems for the main character.

If your antagonist is a person, it's very useful to create a rich backstory to their motivations, because not only will this provide the character with greater depth, but it will also create mystery for the rest of the story. Someone mentioned darth vader being an awesome antagonist and that's because of the rich backstory of him being Luke's father. Avoid the typical cliches of villains who are 'pure evil' and only have self interests (such as wanting to take over the world at all costs) unless there's a good reason for them having those attributes.

I think interesting villains also have their own character arcs. Sometimes, they choose to do evil because their rational brains want them to do it, whilst their feelings and heart oppose that of their logic. This type of opposition between the rational vs. emotional brain is a great opportunity for change to occur.

I agree with Got_Rhythm. I look for a realistic or compelling reason for whatever they are doing. For me, the stories that are truly great demonstrate growth and change in both the protagonists and the antagonists. If you're interested, the following link is a good resource for figuring out what type of antagonist(s) you wish to include in your story: http://tvtropes.org/pmwiki/pmwiki.php/Main/Villains . Best wishes!

What about the Joker then?(the movie ones) He, compared to Bane, is just plain nuts. He made the phrase: "Some men just want to watch the world burn" famous, not because he had an obvious reason behind it, like Bane did, but more so because of his rancid unknown hatred for the world. He is fun exactly because he's a nut crack; or just plain cool at times. He has no redeeming qualities that are known of (except maybe for brains), he's just plain crazy.

You don't need a redeeming quality to make a good, loved villain(although it does help), you don't need to make a believable one, you can imagine a person so twisted as to kill a puppy in front of a child as long as you give him a purpose, keep them cohesive, and give them an actual personality. As long as he stands on his own feet and has a purpose, he'll work.

Another kind of villain that hasn't been mentioned in this forum is the "fallen one" or simply the "good guy" who, tricked or simply misinformed thinks the protagonist is a bad guy, and try to stop him at all costs, maybe even renouncing some of his own former morals. Seeing a paladin fall down to the likes of a cutthroat over something as minor as seeing the wrong man in the wrong place at the wrong time, while devastating, will leave a lasting impression and emotional attachment towards him.

Joker is not just crazy. He actually is trying to show one of the themes of batman overall of "One bad day and you could be just as crazy as you say we(the villains) are". He's also a solipsist where he believes it doesn't matter. That for all Batman and people's belief that things matter and there needs to be order to the world none of it matters and there is no order to the world, just people pretending that it is the case.

I absolutely hate what DC has done with almost all of Batman's villains since the new 52. They gone from having this rich character that is psychologically deep and interesting to shallow crazies that have always been "just crazy". It's irritating as a fan that they are so bad in current cannon.

On the other hand, I highly recommend people should read "Penguin: Pain and Prejudice" which delves into the history and psychology of Oswald Cobblepot.

I think what makes a good antagonist is a character that you understand where they are coming from and can see how they got from a position you could very easily see yourself in to this other position that seems completely nuts... in other words it seems like a good antagonist is a character that makes the Irrational rational.

The antagonist becomes more powerful to me when he is very economic in his dialogue. The "less is more" principle in action. When he is serious, hard to read and has a quick execution of his actions; it makes him unpredictable and therefore frightening.

What I also look for in antagonists is a clear motivation. Anything short of that and the character starts feeling artificial, like he is motivated "because the script says so," instead of because of a believable reason.

Another way to make an antagonist more interesting is to make him of the opposite gender to the protagonist.
Most of the time the protagonist is a male, so a female villain would give room for some interesting directions that you could take in the story and dialogue.