If the template is being created in Microsoft Word, the Auto formatting feature can add formatting information that is not supported by Salesforce. One way to prevent HTML e-mail templates from having extra spaces it is best to either turn off the Auto-Format function in Microsoft Word, or undo the auto-formatting as it occurs.
Another method of removing extraneous formatting information is to copy and paste the text into a blank notepad, and then cut and paste the text into the Salesforce e-mail template editor. Note that this may strip the desired font or formatting, so make sure to proof your template and make changes directly in the template editor.
Alternatively, you can also edit your template in Salesforce and manually type over any affected characters and resave: Try to backspace over the extra line spaces, then press Shift+Enter to remove them.
Finally, the issue could also be due to the encoding used in the template. Try changing your template encoding to UTF-8; this can resolve issues when using languages other than English as well.