
Hi diane,
Intact stamped envelopes are called "covers" and many people collect them. Many people also collect cancellations and postmarks, usually "on cover" but sometimes "on piece", cut from the corner of the envelope. On cover is almost always better. On piece is usually only good if the paper around the stamp is neatly cut, including the whole cancellation, and cut with a generous amount of paper around them both.
The exception may be unusual "fancy cancels" which are cancellations that were made by a postmaster cutting interesting shapes in corks. Here is an example of one of mine:

If the fancy cancel extends onto the paper it is better to keep the stamp on piece to preserve the whole cancellation, even if the paper is more roughly torn from the envelope.
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Karen