This little mindmap found on applicant through Twine summarizes all the various usages of Twitter in a business setting. Full size image here. Five facets are proposed:
Customer service: Twitter as a messaging service
Networking: Building personal relations through conversations
Management: Announcing, reminding, tracking positive and negative experiences, brainstorming…
Traffic: Pulling traffic and sending traffic to specific content on other platforms
Information: Staying current on breaking news (intelligence), sharing ideas…
In my experience, intelligence gathering comes first, but I am not a heavy user of Twitter…