Note that desktop Linux is moving away from running X clients. A daemon (such as udisks) runs with privileged access. When a client (such as your graphical file manager) needs to perform an operation through this daemon (such as mounting a filesystem on a removable device), it asks the daemon to perform the action. The daemon will then check with PolicyKit if this is allowed. Depending on PolicyKit policies, an authentication agent will be invoked (perhaps prompting for credentials in the form of passwords or biometrics). If access is allowed, the daemon will perform the requested action.
All this stuff is done through D-Bus and D-Bus activation. This means you don't need to do anything other than installing an authentication agent. There are authentication agents for KDE and Gnome. Alternatively, add some local PolicyKit policies to allow access to the resources you need without requesting authorization through an agent.
Not all software supports PolicyKit, though. So basically, you have options:
If the program you're planning to run as root supports PolicyKit, you can simply install a PolicyKit authentication agent and just launch the program with your regular account. You'll be prompted for authentication if needed.
If the program you're planning to run as root supports PolicyKit, you can create a local policy so the requested privileged actions are always allowed for you. Then you can just launch the program with your regular account and access will be automatically granted.
Use gksudo or similar programs by prefixing them with gksudo, as joepd described.
Use password-less sudo.
I haven't yet experimented with option 1 yet, option 2 works fine here.
Similar question asked here http://superuser.com/questions/389397/ubuntu-and-privilege-elevation-in-i3wm with solution based on ConsoleKit, though I haven't checked it. p.s. Please, spell question titles correctly with capital letters.