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Producteev, a popular task-management tool, is taking a big step forward, updating its web and iPhone apps (s AAPL) while launching new Android and Windows (s msft) desktop apps. The wholesale improvements, which include TaskRabbit integration, help Producteev in its quest to become a universal task management service as it seeks to work across multiple platforms.

New York City-based Producteev has won raves for its ability to enable task management through existing channels such as email, IM, Google Calendar (s goog), Twitter and Facebook. It is now being used by 1,000 business customers including Orbitz (s oww), Trulia, Boston College and the Financial Times. (s pso) Users can send tasks and receive notifications through various communications channels, then manage tasks through Producteev’s web and iPhone apps, which offer syncing between the two platforms.

Now, Producteev is introducing a Windows desktop app along with an updated iPhone app and Producteev’s first Android app. The new apps provide a redesigned user interface and the ability to create multiple workspaces, set and receive notifications across all workspaces and search across workspaces via keywords. There’s also natural language processing for better task capturing, label auto-sorting and offline task access.

Producteev is also introducing version 3 of its web app, which includes some of the same features including notifications across all platforms, advanced search via keyword, better managing of subtasks and new settings that allow administrators to control who can and can’t join work spaces.

Producteev said it’s the first to integrate TaskRabbit’s API, so users can tap TaskRabbit’s users to complete tasks. This provides more functionality for Producteev users to get things done quickly and gives TaskRabbit a nice way to generate more work for its network of users.

Ilan Abehassera, Producteev’s co-founder and CEO, told me the company, which is close to breaking even, is moving toward becoming a Dropbox or Evernote of task management. He said while other solutions offer a closed environment, Producteev sees value in being on as many platforms as possible.

“By creating an open platform for your tasks, we put your tasks in the center of your daily life, and make sure it’s easier to create a task on Producteev than taking a pen and a piece of paper. That’s how Evernote got successful. If they only had a web app, they wouldn’t have been successful,” Abehassera said.

Producteev faces plenty of challengers such as Basecamp, Asana from Facebook’s Dustin Moscovitz and Trello, from Stack Overflow founder Joel Spolsky. Google also has Google Tasks, and Apple introduced a reminders function in iOS 5. Abehassera said the growing competition highlights the big momentum in the task and project management space and he hopes to stay ahead of the competition by being ubiquitous, robust and yet easy to use.