One particularly absurd one is that
The basic argument here is that money that you put in the bank doesn't sit in the bank, it gets lent out to businesses or home buyers or whatever. The point of their argument is that stimuli which cause people or banks to hold less cash in savings aren't actually stimuli, because they just take money from some useful purpose (being loaned out). This argument is massively flawed on two points. One is that the choice is not really an either/or ; it's not "lend money to businesses" OR "consumer buy things with it", when you buy things as a consumer, the money moves from one bank account to another - it's always in a bank, and therefore can also be used for loans (BTW this does suggest that money held in cash is a big disadvantage to the economy - electronic currency can be used twice while cash money sits and does nothing; and all the people "investing" in gold these days must be very bad for the economy, because the gold is just sitting there). Furthermore, the contention that banks loan out money proportional to their reserves is not quite right. In fact, when there are good prospects for investment, they can leverage up many fold. The idea that businesses wouldn't be able to get loans because banks don't have enough cash is not quite right, because the fed basically gives them free cash to invest whenever they want. In our economy, banks basically leverage up to invest in all the possible money returning investments - their balance sheet is proportional to demand of cash, not supply. The book value of money in circulation can be many times the actual supply of money, and that ratio goes up and down based on the amount of good investments available.
This one is being spread by the Ron Paul anti-deficit types. Their basic argument is that government deficit spending is not a stimulus, because it is just taking money from somewhere else, either by raising taxes or issuing treasuries. They contend that if the money was left where it was it would be doing just as much good because they claim money in savings accounts is "working" (they love to use silly quotes like "money never sleeps"). From the above argument we can see the hole in this - what government spending actually does is create more demand for money, which may be a useful thing in times of low demand. There is the issue of how much utility you get from the government's choice of spending, but it's certainly greater that zero, so government spending is better than no spending. Also, the people who argue this point seem to be intentionally obtuse about the benefit of foreign capital. Foreign capital is clearly a stimulus in the short term; it's more subtle what the long term effect is, but they argue that it's not even beneficial in the short term. If your economy was actually healthy and provided good investment oppportunities, foreign capital would be coming in that way.
"Government dollars from tax-and-spend do not help the economy"
Now that we've gone over the first two, we can address this slightly more subtle point. What actually happens when the government taxes some money and then spends it? The money is not disappearing from the private economy, it is being spent on something which has some utility, and then it goes back into private circulation. The only possible disadvantage is that during that cycle, the money can't be used for other things (because transactions are not instant but rather take time), and if it was left in private hands, during that time it could be spent on something with higher utility. I believe that the measure of "best" we should use is maximizing the total utility to the citizens. So the question comes down to - would it be spent if it was left in private hands? If it would have just been put in savings, then we should see that the government spending is better. Even if private people would have spent it, I believe the issue is whether their utility would be higher than the governments. Now, in theory if people are rational actors, then being able to make their own choice about how their money is spent should result in higher utility (this is the basic theory behind free market capitalism), but that isn't always the case. For one thing it can happen simply because individual spenders don't have the same choices as a collective force like government; eg. government can buy health care with negotiated prices and force prescription drug makers to void patents (not that the US does this), things that individuals could not.
I started thinking about all this because I was thinking about Christmas spending. It's often said that Christmas spending is a big stimulus to the economy. But is it really? Let's say there was no Christmas, people would still buy lots of things they need, but they would make better choices about it. Christmas forces you to spend a lot more than you might otherwise, and also to buy lots of things that the recipient doesn't really want - these are near zero utility purchases (not quite zero, because the satisfying the social obligation of giving a gift is a form of utility).
It seems obvious to me that instead of spending a thousand dollars on Christmas presents that nobody really wants (low utility), the world would be better off if we took that Christmas money and gave it to the government to spend on roads, transit, schools, etc. - things that will actually help us all.