To prevent possible loss of data, Excel cannot shift non blank cells off of the worksheet

What:

Microsoft Excel on Windows 7

Problem:

When trying to add new row or column Excel returns following message:

To prevent possible loss of data, Excel cannot shift non blank cells off of the worksheet. Select another location in which to insert new cells or delete data from the end of your worksheet.

Solution:

You have reached maximum number of rows or columns in worksheet.
It is possible that formatting was applied to whole worksheet, i.e. border

Put your cursor into row A, into first empty column.
Hold down left Ctrl+Shift+End to select columns up to the end.
Go to Edit > Clear > All or in latest Excel on Home tab select Clear > All

Need to do the same with rows, put your cursor into column 1, into first empty row.
Hold down left Ctrl+Shift+End to select rows up to the end.
Go to Edit > Clear > All or in latest Excel on Home tab select Clear > All