AWS has announced the general availability of the functionality to Monitor Estimated Charges Using Billing Alerts via Amazon CloudWatch as of May 10, 2012 (which according to Daniel Lopez' answer [+1] has been available to AWS premium accounts since end of 2011 already):
We regularly estimate the total monthly charge for each AWS service
that you use. When you enable monitoring for your account, we begin
storing the estimates as CloudWatch metrics, where they'll remain
available for the usual 14 day period. [...]
As outlined in the introductory blog post, You can start by using the billing alerts to let you know when your AWS bill will be higher than expected, see Monitor Your Estimated Charges Using Amazon CloudWatch for more details regarding this functionality.
This is already pretty useful for many basic needs, however, using the CloudWatch APIs to retrieve the stored metrics yourself (see the GetMetricStatistics API and Getting Statistics for a Metric for usage samples) actually allows you to drive arbitrary workflows and business logic based upon this data.
Regarding the latter, the scope of this offering is stressed as well though:
It is important to note that these are estimates, not predictions. The
estimate approximates the cost of your AWS usage to date within the
current billing cycle and will increase as you continue to consume
resources. [...] It does not take trends or potential changes in your AWS usage pattern
into account. [emphasis mine]
