What if you send some illegal stolen money?
Here's a scenario. Politicians in the U.S. cannot accept campaign donations from foreigners. So what if a politician has a static Bitcoin address for donations and then a payment arrives anonymously? How does the politician know the funds did not come from a foreigner?
The solution to that is for the campaign to not use a static Bitcoin address but instead to issue a new Bitcoin address for each donation. That way they at least they can ask for information identity that can be associated with each donation's Bitcoin address.
That doesn't stop someone from sending stolen funds, but it squelches the problem for the recipient in most instances.
Further, if the receiving of payments is a sensitive issue for you or your organization, what you can do is ensure that the person paying you maintains (or forwards to you) the payment protocol signatures on the payments they've received for the funds being sent to you.
The new Payment Protocol is a feature being added to the Bitcoin-Qt/bitcoind client (targeted for v0.9). With it the party to be paid issues a payment request for each payment to come from the sender. This way you can at least prove that the party sending you funds has an audit trail showing that the funds were truly sent to them (versus those funds coming from illicit source, such as if they snagged the money from a wallet obtained through malware, for example).
FAQ on the payment protocol -
http://bt.irlbtc.com/view/300809.0