What the new API will do is allow third-party developers to integrate Google Tasks into their own tools, so you'll be able to sync your to-do lists between Google Tasks and a variety of popular productivity and project management apps. So far, Google has announced four outside apps that have started using the API in the last few weeks: Producteev, Manymoon, Mavenlink, and Zoho.
Notably, three of these four apps are from the project management space, which should give us a clear indication of how Google and other developers view the relationship between Tasks and third-party tools. Tasks will serve as a simple satellite to the specialized project management services, putting prioritized to-do items within plain view in Gmail and Google Calendar, while preserving the primacy of the project management app for more complex work.
Producteev, by contrast, is a personal and group to-do manager that stands alone or plugs into Google Apps. So while project management apps have the early lead in GTasks API integration, we could see this API pop up a host of mobile and Web apps over time, in much the same way as Toodledo syncing has become a staple feature in many mobile apps over the past year or so.
While I'm not aware of any major announcement from other software companies, users of and other popular to-do apps are already clamoring for the developers of those apps to get this API added in. Bringing Tasks syncing to such apps would likely be a far better solution than the existing Gmail plugins that many such Web apps currently feature, opening a two-way communication path between Gmail and Google Calendar, and the apps we've all grown dependent on to track our next actions.
It's worth wondering whether Google Tasks is now set to overtake other productivity tools in the marketplace. For the most part, I doubt it. I see no evidence that Google is building out Tasks with the depth of functionality that would be required to unseat Toodledo and RTM, though users of low-complexity task tracking apps might very well make the jump.