Emo Phillips suggests an elegant way to prove this: Take a sheet of paper, tear it in two, jettison one half. Repeat until you have a single atom, tear again, and you should get quite an explosion.

Don't you love it when your friends contribute helpful suggestions, Kirk?
It's hard to think of one, because most matter is composed of molecules, not mere atoms. Even elemental substances are made of molecules-- the air you breath contains N3(?) and O2 as well as compounds like CO2, so you can't just grab oxygen from the air and have oxygen atoms to play with, because they've bonded into molecules of oxygen. I suppose the noble gasses (helium and neon are probably the easiest to obtain) are naturally in atomic form, I don't know how you'd take advantage of that.
I'd settle for proof of molecules.
Wow. . .sounds like you're out to prove something, Kirk.
Well, it's funny, for all my trust in the skeptical "show me" process of science over the "I believe!" mandate of most "faith", there's a lot I take my high school science teachers' word for.
In some ways, there's not necessarily wrong with taking these things for faith when we're not necessarily specialized in it. Otherwise, imagine, in our complex world, how individuals wouldn't get too far if they wanted to try understanding everything that's proven.
Then again, by taking something on faith (which I wish more people did with traffic law), the powers that can be can screw us over. . .. I'm kind of exploring this idea on my Blog at http://thelex-topia.blogspot.com .
BTW, you've got a nice Blog here. =D
The only experiment I recall that's proof of molecules is the demonstration of Brownian motion, but I don't know how you'd rig it up in your home, considering that it requires massive magnification of very small particles. The demo I saw in college physics featured a specialized apparatus that could project onto a screen the individual particles of smoke (from a burnt match) that had been drawn into the apparatus. Per wikipedia, the discoverer and namesake, a biologist named Robert Brown, was observing "minute particles within vacuoles in [grains of pollen]" that were floating in water. The subject particles have to be small enough to exhibit this random motion caused by the impacts of randomly moving molecules in its medium, generally liquid or gas.
Any most fans of the HHGttG Infocom game are also familiar with the brownian properties of hot tea, and its utility as a randonimity generator when coupled with an atomic vector plotter.
On the other hand, it could be that only a comprehensive study of chemistry could convince one. I realized recently (when I was watching Tommy Lee: Back to School) that the periodic table is one of those massively data-filled charts, both in printed info as well as in its very organization, and that if you have enough chemistry knowledge to understand each of its fields and axes, then you would be hard-pressed to deny the existence of molecules and atoms. The periodic table is really an amazingly elegant summary of a complex theory of molecules or chemistry or atoms, and while it only alludes to the properties of the nuclear forces, and doesn't necessarily scale up to things like states of matter and crystalization-- that is, it doesn't entirely predict the properties of elements or compounds, it does make spot-on predictions about the behavior of both to each other. If only they could add a thermodynamic axis or something.
My only regret is that I came to realize this while watching a moronic has-been musician make an ass of himself for reality TV. I wasn't an inattentive chem student or anything, either. It just now came together.