I suspect that the 'new basecamp' will be a seamless integration of Basecamp, Campfire and Highrise with one simple API where people can extend it to whatever level they wish. So Basecamp 2.0 will be a project management platform. Maybe an SAP and Salesforce of Small Businesses?
Adding to the above, I also assume they would be the first major app that would be fully acessible via the browser. Maybe 'kill' the need for the app store?
We did something like that in mid-2000s as an Open Source project (http://openpsa2.org/). Never really caught fire with us, though. Business apps are a difficult area.
Open Source and Free do not work for serious businesses.
For open source, you want someone responsible. Except you have a strong re-seller and support program, I doubt it will work.
Free is an entirely different issue. A business will not want to be 'Gowallad'. i.e, Sell suddenly and say have your data and thanks for your time. We are shutting down next month. See thread discussing this http://news.ycombinator.com/item?id=3318458
When you create a company i.e charge money, businesses know you are serious and have someone to complain to. Then you have a higher chance of gaining traction.
Open Source and Free do not work for serious businesses.
That is probably a too extreme take on this as well. Open Source is a great "insurance policy" for companies, but not enough on its own. You also want a company dedicated to supporting and developing the software that your company uses so that you can have a proper contractual relationship into it.
For example, MySQL AB was running quite a good business supporting the freely licensed database for companies using it: http://en.wikipedia.org/wiki/MySQL_AB
Adding to the above, I also assume they would be the first major app that would be fully acessible via the browser. Maybe 'kill' the need for the app store?
I look forward to what it would be.