Shoutbox

Pulling out the small wire connection on the motherboard is the only and best solution, as Adeptus already said....

It is also extrememly easy and you don't do any damage to anything. (sticking tape can leave residu, it is also ugly, and (quite frankly) stupid todo if all you need to do is open the case for half a minute and disconnect the two wires from the motherboard... You do NOT need to cut anything at all (like Dr4g0n suggested), you only need to disconnect a small connector... Just for info: you even don't need to turn of the pc, but I do NOT recommend doing it without turning it off though)...

Open your case, locate the hard disk light and notice the two wires (usually red and black) connected to it. Follow those wires to the small black connector on the motherboard (sometimes also has "HDD" printed in white on it), pull it out... close case, done.

(the same can be done for the power light, the reset button and the internal speaker)

But note: having a hard disk light can be very usefull. Especially when you need to diagnose problems. And by the time a problem occures it is already too late to connect the light again anyways.

It can also be very usefull to detect dubious hard disk activity. eg: all of a sudden your HDD starts to do a masive amount of stuff = this can indicate virus activity (eg: HDD is being formatted or erased!)... Or every second your hard disk light lights up, this can also indicate malicous activity which you would otherwise not notice... Etc.