I've made wine! (Though not in a long time now.) You're right, it is fascinating- not only the process itself but also the wide range of wines that can be made. I can still remember the hours spend gathering dandelions for dandelion wine.
Definitely even more accessable to anyone (and I actually think more delicious) is making hard cider. If you are really interested in learning the art of fermenting drinks this might be a good place to start. All you need is some non-pasturized cider (or apples and a juicer), some fermenter's yeast (actually even bread yeast will work- but it will change the flavor), perhaps a little sugar, a container, and a release valve. You can even double-ferment it for cider champagne (though you'll need a few peices of bottling equipment).
You can find lots of free instructions on the net- I really encourage you to give it a go. Good luck!