In both Excel and Google Spreadsheet...
- Enter a date in a cell
- With LEFT mouse button, click (and hold) square handle in bottom right corner of cell.
- Drag the selection to cover all cells you wish to be dates.
- Release mouse button.
However, Google Spreadsheet will fill the selection with the same date, unlike Excel that fills a sequence of consecutive dates.
To make a sequence of dates in Google Spreadsheet, complete the first two cells manually and select these two cells to drag over the required range of cells. Google Spreadsheet then continues the sequence.
UPDATE 3-Jun-2020: Not sure when this behaviour changed, but you now only need to select a single date before dragging to create a sequence of dates increasing by 1 day. In this respect, the behaviour is now the same as Excel.
Note that you do need to make sure you have selected the appropriate locale and date format for this to work as intended. See the following WebApps answer for more detail on this.
In Excel, enter a date, hold right click button + shift and move the mouse to create dates
This does not work for me in Excel?