No, Mitt Romney, they're not really.  They're completely unlike people in almost every way.  They may, however, involve people, real people, at some stage in the process.  But this doesn't mean the corporation simply is the people who work there.  That would be, er, communism or socialism.  In a recent add, Romney says:

At just over the halfway mark, Romney declares: "Businesses are comprised of people. I'm talking about repair shops, and gas stations, and beauty salons, and restaurants. I'm talking about Apple computer, and Facebook, and Microsoft. I'm talking about businesses that employ people. It's really astonishing to me that the Obama folks would try and argue that businesses aren't people. What do they think they are? Little men from Mars? But when they tax business, they tax people."

Well, this is different from "corporations are people."  But it's still equally wrong.  It's wrong now because repair shops and gas stations really don't belong in the same category as Microsoft, etc..  More to the point, the problem with this new formulation is positively Clintonian–it depends on what the meaning of "is" is.  Corporations involve people; sometimes lots of people, transnationally.  But they are certainly not identical with them in the narrow sense of identity Romney seems to suggest.  Anyway. 

On this same point, here is an epic Iron Man (by a liberal commentator, of course–it's a disease they have) of Romney's argument:

Matthew Zeitlin has a nice New Republic post on the Romney “corporations are people” clip and the very real “hack gap” between Democratic and Republican parties.

The title of my own comment on this imbroglio, Separating the wheat from the gaffe, telegraphs my view. What Romney said is obviously true, and everyone who thinks seriously about economic policy understands it. Taxes on corporations fall on the owners of corporations and on other stakeholders. On the specifics, this particular attack on Romney is devoid of substance.

So the taxes fall on their "owners" (who sometimes aren't even actual people), but this doesn't mean corporations are people too.  It means, at some level, they involve people.  No one denies that.  They object to the way they involve those people.