This is a common issue with Office 2007/2010 as well on Windows.
You could try opening up the signature within Outlook to be edited (directly in Outlook, not in Word) and remove the spaces.
But you should try this first:
Close Office 2011/2010 (whichever suite you're using).
Find the default template for Word & Emails (html-based) = usually Normal.dot(x) or NormalEmail.dot(x).
- save what you want to put in a Signature - plain txt, then delete the signature.
When you launch MS Word it'll rebuild Normal.dot(x) file.
close
When you launch a new email it'll rebuild NormalEmail.dot(x)
Close the new email.
Now create a new signature, from within Outlook (ensure double-spacing, font size, font colour, bold/italics/underline - whatever you need is basic.
Test the signature input - if its too your liking, then create a NEW signature (keeping the new one just above) and add what you require to be special with it. Test that.
Cheers.