I'm just trying to take down the voltage of a 9v battery to around 5 volts, so I'm using a 180 ohm resistor. When I use my meter to test the resistor, it reads 180 ohms as expected, the same for the 9v batter who reads about 9 1/4 volts.
The problem is when I test the 9v battery with the resistor, it still reads 9 1/4 volts, as if the resistor isn't even there. What is going on?
A single resistor is only limiting current not voltage. To effectively reduce the 9V to a stable 5V you'll need a voltage regulator like the commonly used 7805.
What you need is an understanding of... (dramatic music) ohm's law!
so basically you have the following equation: I = V/R, where I is current in Amperes, V is voltage in volts, and R is resistance in Ohms. When you increase resistance, you decrease the current in the circuit, while the voltage remains the same.
Resistors don't change voltage; they change current.
Aaarrggg.
The world has been lying to be this whole time...
Now there is a method of using a couple of resistors to reduce the voltage. Its called a voltage divider.
But there are drawbacks.
The voltage output of a voltage divider is not fixed but varies according to the load. To obtain a reasonably stable output voltage the output current should be a small fraction of the input current. The drawback of this is that most of the input current is wasted as heat in the resistors.
So the 7805 voltage regulator will work for me taking 9v down to 5v?
Yes. That's what its designed to do.
So the 7805 voltage regulator will work for me taking 9v down to 5v?
Does a bear go to the bathroom in the woods? And that is not no lie. 
Lefty
If you want to get the full 1 amp rating for the 7805, you -must- mount it to a heat-sink (unless you like having smoke/fire-emitting devices around!)...
How big a heat sink is required? I've just built an arduino on a stripboard with a 7805, to go into a robot in the end. On full load the entire bot might pull about 1.5A on full load (6xI think about AA batteries). Are we just talking about some copper with fins on it or something more substantial?
Oh and another question now that I think about it - would having less of a voltage difference going through the regulator mean less heat generated?
On full load the entire bot might pull about 1.5A on full load (6xI think about AA batteries).
You're not powering the motors through the linear reg are you?
would having less of a voltage difference going through the regulator mean less heat generated?
Yes defiantly.
about 1.5A on full load
The 7805 is only rated for 1A. Can you power the motors direct from the battery to save having to waste a lot of heat.
How big a heat sink is required?
Very difficult question to answer without knowing so many other things. See:-
http://www.thebox.myzen.co.uk/Tutorial/Power.html
Ahh, that's a point 
Yes, the motors are driven with the full 9v through a driver chip which will take power from the input line rather than past the regulator. Ok then, no probs. I must be tired, I've been making the stripboard arduino and got used to the idea that 'everything' is past the regulator. Forgot about driving the actual motors
If you need more than 1 amp, and all you have are 78XXs laying around (and are cheap and lazy like me!), you can parallel the lines together for higher amperages (I would only 2-3 like this, honestly - it would get absurd after that).