George Washington
At the end of his second term, Washington retired for personal and political reasons, fatigued and disgusted with personal attacks, and to assure a truly contested presidential election could be held. He did not feel bound to a two-term limit, but his retirement ultimately set precedent. The two-term limit to the presidency was formalized with the 1951 adoption of the Twenty-second Amendment to the United States Constitution. Washington is often credited with setting the principal of a two-term presidency, but it was Thomas Jefferson who first refused to run for a third term on political grounds.
1970 United States gubernatorial elections
New Mexico also had a two-year term for governors until 1970, when the state constitution was changed to a four-year term for governors-without being allowed to have two consecutive terms. 
As for the "no two consecutive terms" rule, that was still on the books until 1991, when thanks to a change in the state's constitution, Bruce King was eligible for two consecutive terms. King was elected to the first of three non-consecutive terms.