QGIS allows for opening very many different file formats.
Some of these are directly editable. It is possible to open the data/file, immediately edit the data in QGIS, then save back to the original file.
Many formats can be opened/read, and at the same time it is possible to save/write to that format BUT these require that the data is saved into a second format before editing is possible. This is fundamentally different from the first situation.
The question is what data formats are directly editable by QGIS (the first situation as opposed to the second)?
Reasons a list is helpful...
I think that sometimes QGIS doesn't handle this whole issue terribly well - for example in the past I have had some Excel files look like they are editable but the process ultimately fails - which adds confusion.
Notes at gdal.org provide some information, but it can be very difficult to distinguish between the two situations above - formats which are directly editable, and on the other hand formats which can both be read and written (but aren't directly editable).
It is helpful to have information about QGIS (or ogr) version in answers.