I recently discovered this limit the hard way, after being charged a fee for each transfer over the limit. With online banking becoming so prevalent, this is a huge inconvenience as it prevents people from structuring their savings for the best internet rates. What is the reasoning behind this rule?
The regulators (in the past, at least) and banks distinguish demand-deposit (checking) accounts from savings accounts. Checking accounts are without such limits, but savings accounts are subject to withdrawals-per-month limitations. The overall effect of this is to slow the speed with which money flows through the savings account, thus essentially making the money remain on deposit for a longer time. That's exactly why generally savings accounts pay more interest than checking accounts.
Savings accounts aren't transaction accounts, so FRB Regulation D (bstpierre linked to it above) disallow more than 6 withdrawls per month. You can deposit all that you want.
Traditionally, folks who have wanted to maximize earnings for a transaction account would get a money market account. In 2011, rates are so pitful for checking, savings and money market accounts that it is pretty much a waste of time to worry about it.
While the other answers are correct in that the banks are simply complying with the regulation they leave out the reason it is a regulation in the first place. The reason is that the reserve requirements are different based on the type of account. This is intuitive because you would want your bank to have more reserves on hand to satisfy your checking account than you would for them to satisfy your savings account. To prevent banks from giving savings accounts the same features of checking accounts (thereby making them savings accounts in name only) the regulations require restrictions on the features of savings accounts.
Workaround: Carry just enough in your checking account for normal needs, and use online banking or ATM or scheduled transaction to do an inter-account transfer periodically to refill that. My checking account rarely goes over $3k, and that's usually right after the automatic transfer in that funds the mortgage payment. I could run it much lower, but I dislike having to make transfers at the last moment to make sure a check will clear.