The best-known example in the English language is the Great Vowel Shift, which began in the 15th century. The Greek language also underwent a vowel shift near the beginning of the Common Era, which included iotacism. Among the Semitic languages, the Canaanite languages underwent a shift in which Proto-Semitic *? became ? in Proto-Canaanite (a language likely very similar to Biblical Hebrew).
A vowel shift can involve a merger of two previously different sounds, or it can be a chain shift.
One of the several major vowel shifts that is currently underway in the US is the Northern Cities Vowel Shift. This change pattern is characterized by the longer and lower vowels moving forward and upward, while the shorter vowels move downward and backward. This vowel rotation, for example, is noticeable as the vowel sound in "coffee" is moving toward the vowel in "father." While there are undoubtedly several other change patterns that define the shift in the Northern Cities, they are diffusing throughout the North in a unique manner, and are inherently different from dialect shifts taking place in other regions.
In addition to the Northern Cities Vowel Shift, the dialect change patterns that are taking place in the South also indicate undeniable pronunciation changes in the region. In contrast to the changes in the North, however, the Southern Cities Vowel Shift is characterized by the shorter, front vowels moving upward and adopting the characteristics of traditionally longer vowels. To exemplify this Southern vowel change, the vowel in the word "bed" is commonly used, as the "e" moves upward and gains a glide and causes the word to be pronounced more like "bayd."
Wolfram, Walt, and Natalie Schilling-Estes, American English: Dialects and Variation, Oxford, UK: Blackwell Publishing, 2006