Are there any examples of U.S. Federal Government agencies offering service level agreements (SLAs) for their APIs?
SLAs suggest a quality of service that costs money to maintain ... in the business world, you have to pay to get an SLA.
The only time that I've been involved with something approaching an SLA would be an MOU (Memorandum of Understanding) between two federal agencies. In some cases, the agency requiring a given level of service helping to pay for the upkeep of the network and processes that go into making the data available ... in others, it's just an agreement that the connection to retrieve the data exists, with no guarantees on availability.
(Disclaimer : I work for the Solar Data Analysis Center, but I'm not the 'Joseph' listed on their website; I'm also not involved with these MOUs, other than knowing that they exist (and which hosts not to block if they start acting up))
There is a growing list of US government APIs on Data.gov (about 500 at this time). These are available without any SLA required. Additional resources and best practices for US government APIs will be added to this site over time. If you are interested in using APIs and asking whether you have to sign an SLA to do so, the answer is no, the US government provides this freely and without restriction. (Attribution is always appreciated though.)
However, if you are interested in SLAs because you want to understand if there are any changes to an API you are using, that is slightly more complicated. Some of the APIs may have a way to subscribe to related information, and in the future there will be an API key registry (later in 2013) that will help to prompt notifications to consumers of the APIs.