The alchemists' dream (one of them, anyway) was always to make gold. We now know there are very good reasons they couldn't: since gold is an element, making it from anything that doesn't contain gold(*) requires you to change the nuclei of the atoms involved, while all the alchemists had access to was the electron shells around the atom(**). So their efforts were basically hopeless. Now, though, we do have the ability to manipulate nuclei, and in fact we do so on industrial scales. So could we make gold? In fact, let's be more ambitious: could I make gold in my basement? The answer is, surprisingly, yes.
First of all, the easiest nuclear reaction to go for is to transmute mercury into gold. Mercury is commercially available (though somewhat encumbered by very sensible environmental concerns) and not actually very expensive - on the order of $18 per kg (***). Gold, by comparison is more like $40000 per kg. So there's room for some profit here.
How could I make the nuclear reaction happen? This particular reaction needs so-called "fast neutrons", that is, neutrons that are still zipping around at the high energies typical of nuclear reactions, as opposed to neutrons that are bouncing around at energies consistent with room temperature. I could stick the gold in a "fast breeder reactor", but I don't actually have one in my basement, and they're kind of hard to build. I could use a particle accelerator to generate some neutrons (basically by bashing nuclei around until some neutrons fall off) but while I do have a particle accelerator in my basement, it takes one a lot more serious than I can reasonably build to get neutrons out. Nuclear fusion reactions give out neutrons, though, so all I'd have to do would be to build a fusion reactor in my basement. Improbable as it sounds, this actually is feasible, provided I'm not trying to get any energy out.
The trick is that there's a fusion reactor, called the Farnsworth-Hirsch fusor, that is surprisingly simple to build. It is actually something of a cross between a fusion reactor and a particle accelerator: I'd set up an electrical potential in a spherical configuration, accelerating deuterium ions towards the center, where they'd crash into other deuterium ions, occasionally hard enough for fusion to happen. This fusion would release a fast neutron.
To make gold, then, all I'd have to do would be to build a fusor, surround it with a blanket of mercury, run it for a while, and then extract the gold from the mercury. Simple, really.
Let's look at the economics, though.
Suppose we want to make a kilogram of gold, giving us $40000. We need about a kilogram of mercury, costing $18. We also need about 5 g of deuterium (assuming perfect efficiency), which would cost about $30. Finally, we need the power to run the fusor. That's not going to be cheap. An optimistic number for the best fusor ever built is about 10^12 neutrons per second from about 4 kW input. That amounts to 9*10^14 neutrons per kilowatt-hour. Assuming perfect efficiency again, we need about 3*10^24 neutrons for our kilogram of gold, or 3 terawatt-hours, about the world's total energy production for an hour and a half. At $0.10 per kilowatt hour (I live in the land of cheap hydroelectricity) that's three hundred billion dollars.
There's a somewhat more disturbing possibility, though. Gold is easily obtained; you can just buy it. But as a global society, we try very hard to make sure you can't easily get plutonium, particularly plutonium-239, since that is well-suited to building atomic bombs. (You can make bombs out of uranium too, but that requires you to separate the different isotopes, which are very nearly chemically identical. Plutonium, on the other hand, can easily be separated from uranium since it is a different element.) Uranium isn't too hard to come by, especially "depleted uranium" (uranium with most of the uranium-235 removed) - armies fire the stuff at each other, for example. And if you had lots of U-238, a fusor would let you make plutonium out of it. The cost would be high, hopefully prohibitively so, but you could do it without doing anything that would put you on the radar of the IAEA. Fortunately, the power use is so outrageous we don't really need to worry about it.
So, in short, I could make gold in my basement, but not any appreciable quantity, and not for any kind of sensible price.
(*) Since gold is a noble metal, there aren't many chemical compounds that contain gold; unlike, say, iron, gold is often found on Earth as lumps of raw gold. So while in principle alchemists could have started from some gold compound and gotten the original gold back, this would not have been a very interesting accomplishment.
(**) There are actually situations where you can affect the nucleus by manipulating the electron shells. For example, if an isotope decays by electron capture, you can drastically slow down its decay by stripping away all its electrons. But stripping away all the electrons from a reasonably heavy element is one of those things that's virtually impossible under terrestrial conditions but not too rare astrophysically. In any case this has no effect on stable isotopes.
(***) Canadian dollars and American dollars are equivalent to astronomical accuracy.