Both Gnome and Qt/KDE desktops have project management applications of their own such as Planner (the Gnome version) which is an Opensource, powerful app. But as far as I know, unless you have a separate cloud account, you cannot sync data with across Internet using Planner since it's a "software" rather than a commercial application (welcome to correct me if I'm wrong).
In that case if you're willing to pay a little price-tag and looking for a professional project management software for GNU/Linux, then DAISHO is one of the best ones out there. They also have an interesting Philosophy of their own as well. It's a Japanese word meaning the "two swords of the Samurai", representing the discipline and the total devotion to the art.
Anyhow, the GUI is written in GTK tookit, although the MS Windows and Mac OSX version aren't free but the GNU/Linux is completely free of charge!.
But if you want their cloud service, then you'll have to pay but to use it as an off-line utility to manage your projects, nothing's going to cost you!.
*. A powerful time management features (calendar and a separate planning app).
*. E-mail handling (easily integrate web-based e-mail accounts via POP3/SMTP protocols + SSL encryption support).
*. Easy to use interface with Dashboard.
*. Multiple project handling.
*. Plan, set milestones/goals, to-do list and track the progress, etc.
*. Compose reports easily.
*. Import contacts from Skype and Outlook (save files to .csv).
*. If you have installed Skype, then you can make direct calls from DAISHO GUI which should open the Skype automatically!.
*. If you use a Netbook, then Daisho even has an interface that's optimized for Netbooks (smaller screens in general).
These are just a few to mention. You can easily install DAISHO in Ubuntu 11.04 Natty Narwhal (on in GNU/Linux in general, may have to install dependencies first depending on your distribution) by first
1. Downloading the compressed package from this page (both 32/64 bit versions are available).
2. Now extract the content, say to your desktop.
And open the folder and located a file called "Daisho_Installer.sh". In Nautilus, you can either double click on the file and when asked choose "run in Terminal" or just open the Terminal and change the directory to the extracted folder and enter the below command (both ways should work).
They have an excellent installation instructions page if you want additional information.
The rest is pretty easy to follow and semi-automatic thanks to the GUI installation wizard. So as a final word - if you're looking for a professional solution since most the free versions do lack features such as data syncing across multiple source via cloud service, etc then DAISHO is a very powerful project handling/management software without a doubt. Good luck.