I noticed that whatever is in /etc/profile seems to take precedence over stuff in my ~/.bashrc file. How do I make it so the /etc/profile stuff is executed first... and then my .bashrc?

Nope, MDesigner, not sure you are right.
Simply try it. Put "myname=John" in your .bashrc, then logout, login, and echo $myname.
Several things you cannot change in .bashrc, but most of them you are free.

I read somewhere that ~/.bashrc is not automatically read when you start up a bash shell. /etc/profile and ~/.bash_profile are the only files automatically included. I'll have to go find where I read that. Anyway, if that is the case, then you need to explicitly tell bash to include your ~/.bashrc. You can do that easily enough by adding this to your ~/.bash_profile:
If your system has /etc/bashrc, then you can probably see an example of the code above in /etc/profile manually including the contents of /etc/bashrc.

Just as a side note, a single dot ('.') is an alias for the source command, and it might be used in /etc/profile.

Ahh.. duh! It's .bash_profile not .bashrc Works now..

Now here's something weird.. when I'm on the Linux machine physically, logged into X, and start up a gnome terminal, the .bash_profile does not get executed. Why is that? Which scripts get executed when I open a terminal?

no scripts get executed when u open a term
they execute when you log in

Try logging out of X and logging back in. I don't know for sure, but I believe I ran into this before. I made a change to one of the files and it refused to "take" until I fully logged out.

The only rational explanation I can come up with is that once you log in, maybe X caches your configuration files in memory rather than reading them from the disk each time you open a new terminal.

I could be completely wrong though.... it's been known to happen.

<edit>
Errr... I think maybe scuz and I are talking about the same thing... again, could be wrong
</edit>

Not entirely true. Login scripts (profile, bash_profile) are executed when you log in, but bashrc is executed upon opening a new bash shell, such as an X terminal.

All I have in my ~/.bash_profile is
~/.bash_profile is ONLY for login shells. ~/.bashrc is for non-login shells. The above code makes ~/.bash_profile read all the settings in ~/.bashrc. Then I put all my settings in ~/.bashrc.