Cessationism

When speaking of views regarding "the cessation" of certain spiritual gifts, at least one clarifying distinction is very important: the view that some gifts did cease is different from the view that some gifts (recurringly) do cease.

Warfield/Gaffin-style permanent cessationism

Probably the most popular form of cessationism among non-charismatic Western Evangelicals today is that which says that the supernatural gifts were given to attest to the message and ministry of Jesus and His original Apostles, so with the close of that "Apostolic Age" such gifts likewise ceased. We can summarize this view with the words "did" and "were": the supernatural gifts did cease once for all because the were temporary.

Calvin-style repeated cessation after each recurrence where they are needed

In his Institutes, John Calvin says prophets, apostles, and evangelists "were not instituted in the Church to be perpetual, but only to endure so long as churches were to be formed where none previously existed, or at least where churches were to be transferred from Moses to Christ; although I deny not, that afterward God occasionally raised up Apostles, or at least Evangelists, in their stead, as has been done in our time. For such were needed to bring back the Church from the revolt of Antichrist." Taking the full context into account, it is clear that when Calvin speaks about these offices being temporary, he does not mean that there was one singular period in redemptive history where they were uniquely temporary, but rather than whenever God grants them it is on a temporary as-needed basis. Hence we can summarize this form of cessationism with the words "do" and "are": the supernatural gifts do cease in a given locale whenever the church is sufficiently established there because they are only temporarily needed from time to time and place to place.