This issue has surfaced again (see Krugman and Rowe). I wrote a post awhile back on this, but it was quite difficult (for me at least!), so here is an attempt to restate the key conclusions more directly. Ashok Rao has a post covering some of the same themes as my earlier post. The key point here is that I am going to follow Nick in saying that money is different from bonds because money is irredeemable, but even then the Pigou effect is not a magic bullet that gets us out of a liquidity trap.
How is the Pigou effect supposed to get you out of a liquidity trap? In a liquidity trap nominal interest rates are at zero (ZLB). However pretty well everyone agrees that if by some means the monetary authority could induce higher inflation expectations, then the ZLB could be overcome, because real interest rates would fall, stimulating demand. That is a real interest rate effect. It is what some people think Friedman had in mind when he was so critical of Fed policy in the Great Depression. (I have no idea if this is true.) It is what Michael Woodford argues the Fed should now promise to mitigate the impact of the ZLB. It is what Paul Krugman recommended Japan do to get out of the lost decade. But none of these things is the Pigou effect.
The Pigou effect is when the authorities keep the current stock of money constant, and falling prices mean that its real value increases. The idea is that at some point people feel sufficiently wealthier that they spend more, which adds to demand. For this to work, we have to assume that the nominal stock of money will remain unchanged, unaffected by falling prices. Now you might say fine, let’s assume that. But if you do, you might also agree that the fall in prices is temporary. Simple neutrality implies that if you hold the money stock constant, falling prices today will mean higher prices tomorrow. But we have already established that in that case you do not need a Pigou effect, because higher inflation tomorrow at the ZLB will mean lower real interest rates, and you get the demand stimulus the good old real interest rate route. Furthermore, if people understand that prices will rise, they are not really wealthier in an intertemporal sense, because their extra real money balances will be inflated away. If you like, they save their extra real money balances today to pay for future inflation taxes. 
The alternative case is where future inflation does not increase as current prices fall - as would happen if the monetary authority targeted future inflation for example, and did not raise that target as prices fell. That would imply that the current nominal money stock was not fixed, because to prevent future inflation rising, the monetary authority must at some stage reduce the nominal stock of money - long run neutrality again. How does it do that without raising interest rates? It could raise taxes. But if it did that, then Ricardian consumers would not think of their higher real balances today as wealth, because this would be offset by future tax increases.
The central bank could reduce the money stock by selling some of its government debt. But under the conditions that Ricardian Equivalence holds, that has the same effect. Now the government will have to raise taxes to pay the interest on that debt, whereas before any interest they did pay came straight back via the central bank.
We can sum this up rather neatly, as Willem Buiter did here with the aid of lots of maths, by saying that what matters is the terminal stock of money, not its current value. The government can only make people feel wealthier by printing money if people believe that the increase in its real value is permanent.
We can apply the same reasoning to a helicopter drop. The first issue is whether issuing money to pay for a tax cut is any different from issuing bonds, and in particular does Ricardian Equivalence apply? Now macroeconomists are confused on this (see my earlier post), but here I’m happy to follow Nick and agree that money financing is different, because money is not redeemable. So a permanent helicopter drop of money will tend to increase consumption. To put it another way, the Ricardian Equivalence mechanism does not apply to a helicopter drop.
However there is another, more economy wide mechanism. If long run neutrality holds, and if people understand this, they will realise that their extra wealth will eventually be inflated away, so they are no better off. (Equivalently, their tax gain today will be offset by a higher inflation tax at some point.) But those expectations of higher inflation, if we are stuck in a liquidity trap, will shift consumption to the present, so the helicopter drop increases demand through a real interest rate mechanism.
The bottom line is that we can forget about the Pigou effect as a way out of the liquidity trap, at least in what is now our baseline macro model. What is important for the liquidity trap is expectations about future monetary policy. If monetary policy allows future inflation to rise, and expectations are rational, we can get out of the trap. If they do not, then we stay in the trap until some other force gets us out. That force will not be the Pigou effect.
 What if neutrality does not hold? Neutrality is pretty basic, but for the sake of argument let’s briefly consider this. Consumers are now wealthier, because they have more real money with no future costs to come. However I have the following problem if we stick with intertemporal consumers of the Ricardian type, who only consume the annuity value of any increase in their wealth. When do these agents consume their new found wealth? Any answer except never appears to violate consumption smoothing.