Twitter is an excellent tool if used properly and here are few ways throygh which you can harness the power of twitter:
1 – For Marketing
2 – To search for jobs
3 – To search for employees
4 – Sending news, updates, offers regarding your products and services or website.
5 – Find breaking news
6 – To drive traffic to your website or blog
7 – Generate new ideas through twitter
8 – Get feedback from customers
9 – Use a a reminder tool like for meeting, dinner etc
10 – Lastly most imp. ie make friends 
So these tips will help you to get utmost benefit from the free social tool twitter.