There is a great little circuit for something called a "Drawdio"
http://web.media.mit.edu/~silver/drawdio/ that kids really love, basically it's an astable 555 that makes a noises with pitch proportional to how long they draw pencil marks. (it's a bit hard to explain quickly, just try the video on that website)
I teach middle school aged kids electronics at a local workshop, building things such as that, and I can tell you it's very doable to make projects for cheap that kids can build and understand.
The main issues that I have found is the board on which you lay out projects. Breadboards are expensive, and not permanent. PCBs don't allow kids to experiment with their own circuit designs, and unless you are going to take the time and money to let them design their own boards that might not work and then etch them, it's more trouble than it is worth. We use a more traditional breadboard concept that is just an actual, wooden board. Then we have kids use copper tacks and strips to lay down the circuitry, and then they solder things directly to that.
As other people have mentioned, soldering irons are a bit annoying, and a couple kids might get some mild burns, but as long as you don't mind the initial cost, it's totally doable.
One of the great things about the drawdio project, is it allows you to hook it up to a oscilloscope and show the kids more about sound, or hook the piezo speaker up to a computer and run some FFT software, so they can see and hear how the resistance changes the pitch.
Other things to look into are basic transistor circuits, things with opamps, counters, or things with binary to decimal or binary to seven segment LCD chips.