If you're OK with recording your mic audio and system audio pre-mixed, you could download the free utilities Soundflower and LineIn. Soundflower appears as both an input and output device, and echoes whatever it hears when you send it output to its input. This means that you can set your system output to Soundflower, as well as use LineIn to echo audio from your microphone to Soundflower, and use Soundflower as the audio input to your Quicktime recording.
There is one disadvantage to doing this though: because of latency, you don't want to hear yourself on a short delay as you're talking, which means that since you're piping both your computer's audio and your own audio into the same Soundflower device, you're not going to want to monitor it. Which, in turn, means you won't be able to hear the sounds your computer's making (but they will be recorded).
If you don't want them premixed, you can use the same setup minus the LineIn to record system audio on the QuickTime screen recording, and use a separate app like Audacity to record the audio from your microphone. You'll have to start the recordings separately and align them by hand in iMovie or whatever you're using to edit. If you're doing this and if you want to hear your system audio, open up SoundflowerBed and from the menu bar drop down select the audio device you want to send the Soundflower audio to.
You could use Audio Hijack (per Tetsujin) to capture the audio as needed or you could use a USB audio adapter to do it for significantly less.
I use the Behringer UCA202 Audio Interface with my iMac.
When I needed to record a screencast with the audio from the application, I just used an RCA audio cable I had laying in a drawer similar to the image below. You don't need anything fancy or expensive, just a standard RCA audio cable.
In quicktime, I just selected the USB device as my input:
Now, when I say significantly less, Audio Hijack is about $50 if buying the new license. The USB Audio device is $30 and if you have to buy an RCA audio cable, you're looking at another $5. So, for $35, you get an audio interface that has many more uses than the software can provide (for example, I can hook my Bose Wave Radio to my iMac now) whereas the software doesn't allow you to do that.
Make no mistake, Audio Hijack is good software. This is just another, albeit less expensive, avenue to solve your problem.
Best Answer
I was able to do this by going to Utilities>Audio Midi Setup
Click the + sign to add a new device, choose Create Aggregate Device and click both the Built-In Microphone and Built-In Output checkboxes. Then right click the Aggregate device you just created and choose. Use this for Sound Input. Now this device will appear as in input choice in QuickTime Player X.
Now open QuickTime Player X, choose New Screen Recording and click the drop down arrow. You will now see Aggregate Device as a Mic choice.