how to debug application as root in eclipse in Ubuntu?

1. Enable your user to run gdb as root without being asked for any
   password:
   sudo visudo
   Add the following line after all other rules:
   <youruser> ALL=(root) NOPASSWD:/usr/bin/gdb
2. Create or modify a debug configuration in eclipse to run gdb as root
   e.g. in Run > Debug Configurations > C/C++ Application > YourProject Debug:
   change Debugger > Main > GDB debugger from gdb to sudo -u <youruser> gdb

Update (and warning!):

In his comment nategoose pointed out that this answer should come with a warning:

Enabling a user to use sudo for gdb like suggested in my answer in fact gives admin privileges to him/her which in many cases might be an undesired side effect. I therefore consider the answer appropriate in an environment where it’s not assumed that the user would try to harm the system (e.g. it’s your own personal computer or a virtual machine)

For a multi-(non-trusted)-user environment I think it might be a better idead to utilize unix’ file capabilities to enable gdb to debug an application without the need of admin privileges