For reference, the switch in Palee's second post is actually a DPST switch, which is the easiest way to do what you describe. DP switches operate two separate circuits at the same time, which is what your first post describes. You would hook up one LED to one side, and the other LED to the other side, and flipping the switch would open or close both circuits at the same time. The inset in his pic is a pretty good of visualizing what I'm talking about.
Also, as far as your resistor goes, if you use an SPDT switch as Crazy Jayhawk described, you have the same problem as before: keeping the signal separate. I don't know how much you knwo about circuits, so I'll try to keep this as simple as possible (feel free to ignore what you already know). In order for an LED (or anything electronic, really) to work, it requires two things: power and ground. The power runs through the LED, turning it on, on its way to the ground. If there's no ground, the LED doesn't work. If there's no power, the LED doesn't work. I'm not entirely certain how mobo HDD activity headers work. It could go any of three ways: 1. the header constantly provides power, and only provides ground during activity. 2. The header constantly provides ground, and only provides power during activity. 3. The header provides nothing, but on activity provides power and ground. The last is the least likely, and I believe the first to be the case, but I don't actually know, and it may vary from board to board. AAR, if you connected two LEDs to a SP switch, you'd disable the ability of the header to function properly in two of the three ways. Since your power LED is always on, connecting both to the same power would mean that your HDD LED would always have power--and therefore, in scenario 2, your HDD LED would always be on. If you conected both to the same ground, then in scenario 1 the HDD LED would always be on. That's why the DPST or DPDT switch is better--each LED remains separate from the other, so both work as appropriate. You could still do the regular/dim/off thing that Crazy Jayhawk described by using a DPDT switch, or you could just go on/off with a DPST switch. Make sense?
Almost forgot--as far as what resistor to use goes,
here's a resistor calculator.
Last thing--just noticed the discussion of "prong thingys." On an SPST switch, if the switch is on, then the two prongs are connected. If it's off, they're not. Connecting both wires to one prong would sort of defeat the purpose, because in effect, you'd have soldered the wires together. Put one wire on each prong, doesn't matter which goes where for and SPST, but like I said an SPST can only control one LED.
I'd be glad to tell you how to wire the DPDT or DPST if you decide to go that route, and I'd also be glad to shut up if nobody cares.
Edit: Added "prong thingy" explanation