When I copy a cell using Ctrl + Insert and paste it elsewhere in the worksheet, the formatting is also carried along (such as the cell borders, etc). Is there a shortcut to copy only the contents minus any formatting?
You can use Paste Special (in the edit menu) to specify exactly what should and should not be pasted.
If you have Excel 2007 or later, pasting normally (Ctrl+V) also works; a dropdown box then appears with options to paste without formatting, etc. You can then click the menu or press Ctrl to open it and select options.