For me, the first example that springs to mind when talking about minimal pairs is ship or sheep. This is almost certainly due to the influence of the title of the well known book Ship or Sheep by Anne Baker. The formula is this: take a word, remove one of the phonemes and replace it with another such that it forms a different word. In the case of ship and sheep, there are three phonemes and the middle one is exchanged.
Such pairs are useful in pronunciation teaching for various reasons:
In this article, I would like to extend the idea of minimal pairs to other areas of pronunciation, including features of connected speech and intonation. However, since the term minimal pair means by definition pairs of words differing only by one phoneme, the other pairs gathered together below are not strictly speaking minimal pairs. Hence the vagueness in the title of this article.