KeePass Password Safe is an open-source password management utility. There is a KeePass version for Linux: KeePassX. But KeePassX has fewer features and it's development is slower.
If you don't mind using mono, you can use KeePass instead of KeePassX under Linux. Here is how to do it.
1. Install the required dependencies (mono):
sudo apt-get install mono-devel libmono-winforms2.0-cil
2. Download KeePass.zip (not .exe!) and extract it and use a terminal to navigate to the folder where you've extracted it (or use Nautilus Terminal for an easy way to run commands using the terminal in a folder) and run the following command:
mono KeePass.exe
3. Optional: to create a KeePass launcher on your Desktop or Gnome Panel, select "Create launcher", and enter: "mono /path/to/KeePass.exe", where "/path/to/" is the exact path to where you've extracted the KeePass .zip archive.
If you want to use the Linux version of KeePass - called KeePassX, you can install it via the Ubuntu repositories: search for "KeePassX" in the Ubuntu Software Center.
Thanks to LFFL!