4. Create or extend your brand personality
Ultimately, Twitter is far more valuable for distributing your brand personality than it is for merely delivering your content. Companies that are engaging users on Twitter aren't succeeding just because of the information they supply; it's the voice and style of delivery that makes the difference.
H&R Block is a big company. Few people get warm fuzzies when thinking about H&R Block. But on Twitter, H&R Block has a voice that is approachable and helpful. People are exposed to an H&R Block that expands their perceptions of the brand through tweets such as this:

Similarly, Crocs uses Twitter to express its unique brand personality and get people excited about shoes:

Speaking of shoes, the CEO of Zappos uses Twitter regularly to talk about products, parties he attends and anything else on his mind. His voice becomes the voice of Zappos for Twitter readers:
For more examples, check out Carnival Cruise, Marvel and SmarterTravel.
Social media spaces such as Twitter are where personalities meet. If you come across as a monolithic, faceless organization, you will be ignored. If you take the time to hone a voice and personality, people are much more likely to engage with you. Be real, authentic, interesting. Figure out your voice and jump into the pool.