Hi! A cloud chamber would certainly be cool. Otherwise there's of course also the famous
double-slit experiment, it's quite easy to do today. As a matter of fact, I experimented with this some months ago at home for fun, trying to get the best result with minimal equipment. I was thinking of writing a short guide on this actually, but I haven't done it yet. But here's what you would need:
1. A laser
2. Slits
3. A screen
Some notes on the way:
I used a small pen laser (at first with the power button pressed down by tape or something, but later I disassembled the laser and used an external power supply and a power switch).
There are a number of ways to construct slits; I have tried these (and I preferred option 2):
1. Razorblades and aluminium foil. Paint the aluminium foil black with e.g. spray paint. Glue/tape two razorblades together and cut two parallel slits in the aluminium foil (actually make a number of slit setups, since it's quite easy to tear apart the foil). This is however not the solution I preferred, it's a little tricky and easy to mess up.
2. One "barrier" is equivalent to two slits with infinite width. So you can get an interference pattern by using just a single thin barrier. You can use a hair (40-120 μm) taped up on some frame (I used old dia slides). You can also use a thin copper wire extracted from an electrical wire (paint it black). You can actually also use a lead for mechanical pencils; I tried with a 0.5 mm lead and managed to get a pattern nevertheless. But thinner barriers are better; I preferred hair or copper wire.
3. You can also take one or a couple of needles, paint them black and tape them together. But I prefer option 2.
4. Reflection from a laser via a CD is also supposed to show an interference pattern. I've tried this, but got pretty strange patterns which I found difficult to interpret.
5. You could also buy a slit setup from some science shop.
There are some other issues to address as well; laser targeting, environment lighting and screen distance. It's a little tricky to point the laser perfectly at the slits, so some smart mechanical setup is recommended. The laser can be fixated with e.g. tape or something, but I actually used a small adjustable Lego Technic construction I built for this purpose :). Further, in a bright room the interference pattern can be hard to distinguish. One solution is to "screen off" the screen, e.g. tape up a screen inside a cardboard box or something (the screen can be a simple white paper). And last, the distance from slits to screen will determine the pattern resolution (longer distance->wider pattern). I got the best result with the screen at about 4 meters from the slits. If the screen is too far away, I found the pattern to get too blurry.
I attach some pics from my experiment (I apologize for a lousy camera used by a mediocre photographer);
1. My first crappy setup (but it worked).
2. An adjustable Lego Technic laser cannon.
3. Interference pattern.
4. Interference pattern from shining laser through a thin black cloth. Irregular vertical/horizontal pattern since the threads in the cloth are not perfectly parallel.
5. Pattern (?) from a CD (I can't really interpret that one

).
Here's an instructional video I found (apparently there are special CDs with slits too);
http://www.youtube.com/watch?v=f7wkwJ2tiKg
There's also the
quantum eraser, but this is somewhat more tricky than the doubleslit setup;
Do-It-Yourself Quantum Eraser:
http://www.scientificamerican.com/slideshow.cfm?id=a-do-it-yourself-quantum-eraser
I haven't tried that, but I probably will sometime.