Is there a way I can make things just assume that when I run them I am running them as a privileged administrator (AKA root)? I know it could be dangerous and all, but its a risk I'm willing to take in the name of convenience.
Normally I'd include instructions in an answer, but this is such a bad idea I'll point you to a couple places to read up on how to do this. You can take it from there. Note that when you break your system you can post here again for help, but people will laugh and shake their heads and make reference to pebkac errors, etc.
First, the Ubuntu help page on Root/sudo. Note the three large, prominent warnings.
Here's an Ubuntu Forums user that did something like this and couldn't fix their system.
Keep backups of your data if you do it, and consider the wisdom of trading security for convenience. Maybe put on an old Dead Kennedys album while you reinstall...
If you are only interested in specific things running as root, the setuid bit is the appropriate feature.
By setting this bit, the program will run with the permissions of it's owner. Therefore you can take a program, change it's owner to root, set it's setuid bit, and that program will then run as root with no special intervention.
Some programs in Ubuntu are setuid by default - for example,
> ls -l `which ping` -rwsr-xr-x 1 root root 35712 2011-05-03 11:43 /bin/ping
This program needs to run as root because only root can open a port below 1024 for listening, which is required to listen for return packets.
As noted, allowing programs root permissions by default is dangerous, and is typically reserved for simple, well-audited programs - any program which could be exploited as the result of external input will run the risk of exposing your entire system to compromise, instead of just those areas your user account has access to.