I'm thinking of getting a pack of pirhana common cathode RGB LEDs, and was wondering if I could put one resistor that limits the current to 2V (the lowest voltage of the 3 LEDs) on the cathode. Would this work? Or am I being stupid and forgetting something vital? (See attached picture for badly drawn schematic)
You would probably want all the LEDs at the same brightness. By using one resistor value for each LED, assuming they aren't identical, will cause them to light at different brightnesses. The brightness of each LED is what affects the overall colour when they are mixed. Simply for this reason, I would use three seperate resistors, with the value correct for each individual LED. Resistors can be as cheap as 2p, depending on where you buy them from. For 4p extra, you can have a nicer outcome. 
Onions.
In fact it would not work at all because the LED with the lowest forward voltage (the red one) would stop enough forward voltage being across the higher forward voltage LEDs. So if you wired it up like you showed only the red light will come on.
Also if you want R+G+B simultaneously you'll be wanting a white LED anyway 
Ok, so I should buy individual resistors. Any hints on where I can get really cheap resistors in small quantities in the UK?
The usual suspects, Maplin, Farnell and RS.
Don't go buying them in ones and twos, I would get 50 off each value and start building up your collection.
Probably worth getting E6 values first (100 150 220 330 470 680 1k 1k5 2k2 3k3 4k7 10k ...) or even just E3 (100 220 470 1k 2k2 4k7 ...)
resistor values are not too critical in digital circuits and you can put two in series or parallel for other values. While at it get some decoupling capacitors and NPN transistors too and share the cost of postage (some places have free postage though).
I'm buying a bunch of stuff from RS, so I'll get a bunch of resistors from there. 1.1p each seems like a decent price!
I'm fairly new to electronics, so what counts as a decoupling capacitor. I know what they do, but is there a special type, or is it just a certain capacitance value?
Also, RS sells capacitors in the hundreds, so I'm not sure I want to be shelling out £1.70 to get my hands on 100 1uF capacitors, when I probably need about 10. Is it worth getting 100 of them?
so what counts as a decoupling capacitor
Basically a ceramic capacitor 1uF to 10nF.
so I'm not sure I want to be shelling out £1.70 to get my hands on 100 1uF capacitors
At £0.017 each it is a good price, (or is it £1.70 each in quantities of 100?) you will use more then 10. Small stuff like that I would always get in 50 or 100 off.
It is £1.70 for 100, not each, but I'd prefer not to have to buy that many and get one capacitance value. Also, what would be the use of a decoupling capacitor in a rapidly changing RGB LED?
what would be the use of a decoupling capacitor in a rapidly changing RGB LED?
Exactly where you need it to be to keep the supply stable and noise out of the rest of the circuit. You don't put them on signals you put them on the supply.
but I'd prefer not to have to buy that many and get one capacitance value
But if you do much in electronics you will be using them every time on every chip.
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html
It is £1.70 for 100, not each, but I'd prefer not to have to buy that many
One hundred for less than the price of a pint?
Why quibble?
To put it simply, I'm poor, due to lack of being allowed to spend money. I'll leave that open to interpretation.
So start taking broken stuff apart...
What sort of things have capacitors in? Would there be any in broken digital alarm clocks?
What sort of things have capacitors in?
Everything electronic.
Yeah, but not surface-mount capacitors. Would there be any in an alarm clock?
Try things like old VCRs - they often have through hole components in.