Not every company should be on Twitter, but the vast majority of them should be even if they aren't promoting their brand.
Top 5 reasons your company should be on Twitter:
5. Follow trends (Especially trending topics)
4. Get feedback (Listen to your customers complaints and praises. Act on them.)
3. It makes a great customer service tool (Check out ComcastCares)
2. Set up an RSS feed from twitter to track conversations (Very easy to do)
1. Be proactive in the conversation (Find out what your customers want!)