The worst thing that would happen if you wired up a LED to a 12v source and didn't put the right resistor in is the LED would go pop. It's actually pretty funny to see a normal dim red LED go bright orange, give off smoke and go bang.
If you are at all unsure about putting something in your case then run it off a 12v power adapter first, like the ones you may have to run a router or something. I've several 12v power sources around my house, you probably do as well.
Ok basically it's all about V=IR so you know about that.
The formula is thus.
Supply Voltage - LED Voltage / LED current (In Amps) = Resistor value.
So for a ultra bright orange LED on the bay.
Lenses Type : Crystal Clear
Case Style : Round 5mm
Brightness : 6000mcd (Ultra Bright)
Forward Voltage : 1.8 – 2.2v
Forward Current : 20mA (Typical) 30mA (Max)
If the Supply voltage is 12V, and the LED nominal voltage is 2V, requiring a current of 20mA (0.020A) then.
R = (12V - 2V) / 0.02A = 500ohm. You could choose any resistor value close to this.
+ve wire-----resistor----LED|
-ve wire -------------------|
If you join 4 LEDs along a single wire, (long leg to short leg) say for a fan application (wire in series)
+ve wire-----resistor-----LED------LED------LED------LED------- +ve wire|
-ve wire ------------------------------------------------------ -ve wire|
then you add each LED together to make 8V and in this case it would become..
R=(12V-8V) / 0.02A = 200ohm
You can have mutiple wires off the +12v source as the current draw is tiny.
As I said it would probably be easier to source packs of 10 LEDs that come with resistors suited for 12v applications and wiring to suit that. Otherwise you'd need to buy different resistors for different amounts of LEDs in series.
If I get a chance tomorrow/next day I will make a small LED wiring loom and take pictures as an example.
I have a few 5mm ultrabright blue LEDs along with some large 10mm White ones which I bought for different projects.
Bright LEDs are the best for lighting cases.
Just for fun
http://www.youtube.com/watch?v=wO8PdCBejDs and why we need to use resistors
http://www.youtube.com/watch?v=WLctUO1DGtw The current provided by the PSU, even on 5v line is far too much for a LED.