There are a number of organizations in the US trying to encourage the use of various standards in healthcare, buttressed by US Federal funds. Here's a brief summary of some of them, which glosses over many details. All of this is subject to change at any time depending on both federal and state politics (in the US, some parts of the healthcare system are funded and managed federally, others at a state level). I wrote this for a friend in Germany, and then thought others might also find it useful.
Office of the National Coordinator for Health Information Technology (ONC; http://healthit.hhs.gov/): part of the US Department of Health and Human Services, the National Coordinator has the job of encouraging the adoption of healthcare IT and appropriate standards. It's a relatively new department, founded in 2004. It certifies health IT products according to the standards it adopts, and provides funding for various aspects of healthcare IT, for example as part of Meaningful Use.
Centers for Medicare and Medicaid Services (CMS; https://www.cms.gov/): runs Medicare (health insurance for the elderly as well as younger people with disabilities), Medicaid (means-tested health insurance for those on low incomes), and the Children's Health Insurance Program. CMS doesn't set the standards for the clinical care itself, but they do set standards for reporting the quality metrics for clinical care, as well as dealing with payment for their programs.
Meaningful Use (http://www.healthit.gov/policy-researchers-implementers/meaningful-use): the US version of Meaningful Use is a health IT program that's meant to promote the spread of electronic health records to improve health care in the United States. There are a number of aspects to this program. CMS provides financial incentives to physicians and other eligible professionals, as well as hospitals, to use certified electronic health record (EHR) systems, for example. The other part of the program is deciding which standards are the appropriate ones for the EHR systems to use. This is where ONC plays a role. The project is being rolled out in stages across a number of years. Stage 1 is also called the 2011 edition. Stage 2 was just released; the Stage 2 Meaningful Use set of standards is also known as the 2014 Edition S&CC final rule and complements the CMS Stage 2 of the Medicare and Medicaid Electronic Health Record (EHR) Incentive Programs. There are concrete plans up to Stage 3; any further stages depend on politics and perceived needs.
Health Level 7 International (HL7; http://www.hl7.org): an ANSI-accredited standards developing organization that has members and affiliates in many countries. HL7 creates healthcare IT standards based on an overall architecture. Standards can be normative or information, and go through a period of trial use (Draft Standard for Trial Use; DSTU) before becoming full standards. The list of standards in the DSTU phase is at http://www.hl7.org/dstucomments/. The list of ANSI-approved HL7 standards is at http://www.hl7.org/implement/standards/ansiapproved.cfm, and the list of ISO-approved HL7 standards is at http://www.iso.org/iso/search.htm?qt=HL7&sort=rel&type=simple&published=on. People who are not members of HL7 do have to pay for the standards, but HL7 has committed to making them free of charge in early 2013. Several HL7 standards are quoted in the meaningful use regulations that have been published so far, both Stage 1 and Stage 2.
Integrating the Healthcare Enterprise (IHE; http://www.ihe.net/) is an initiative to create profiles of various standards to improve the way healthcare IT systems share information. They are an international organization with many members and run connectathons to test interoperability of healthcare IT systems both in the US and in Europe. Many IHE profiles and technical frameworks are cited for Meaningful Use. There is significant cross-membership between HL7 and IHE.
Thanks to Bob Yencha for review and suggestions for improvements. Any errors, of course, are mine. After writing this, I do find myself wondering whether there is some rule about three-letter acronyms in healthcare IT. And no, there is no meaning to the ordering of the descriptions.