Do (Free) by Do.com is a free productivity tool for all of your task management needs, but is meant to work even better with groups needing to collaborate on small tasks or multiple projects.
To use this app, you must sign-up for free on their website and receive an invitation. The website and iPhone app sync together perfectly. It does seem to still be in the beta stages, though, so feel free to give them constructive feedback as well. In the future, however, you'll be able to sign-up in the app itself.
Along with just adding tasks and managing projects, you're also able to invite team members to help you with your projects. Do allows you to utilize the things you already use in your workflow. For example, the service integrates Google Docs, LinkedIn, and the ability to use your own contacts to invite people by name or email to join you and your projects on Do.
The best thing about the iPhone app is that it can send you notifications, as well. Whenever someone comments on, assigns, or completes a task you can be alerted on your phone.
You can't do everything with the app that you can with the Web interface. For example, when you start the app up, one of the tasks they have added as an example is "upload a profile picture by clicking the image next to your name." However, you can't do so in the app. You can't seem to adjust any other profile settings either. This must all be done on the Web.
Those are just some things unavailable in the current version of the iPhone app. It seems it is still very limited, but you are able to customize and do everything you need to do on their site if you're unable to do so in the app.
Do is a free app in the App Store. Although the app itself leaves a lot to be desired, it's well-designed and shows a lot of promise.
The Web interface allows you to do a lot, especially if you're working with teams on certain projects. So, my advice is to really explore the Web interface and see if it works for you and your team. There are updates coming to the service in general, and definitely the iPhone app. So, if the website works well for your purposes, you'll want to keep an eye on this one.