AWeber is down right now and has been experiencing issues all morning. So, I just discovered a major disadvantage of enabling the click tracking feature on emails: When their server goes down the links in the email break. I don't know if it works this way with other email marketers but would be curious to know.
Click tracking is important if you want to know how well your emails convert but it is something best done from your own domain or from a stats gathering service like analytics. AWeber employs redirects so the links to your content actually point at AWeber first. What you want is for the links to point at your content. You can track these links using parameters inserted into the URLs directly.
If you track in this way I strongly suggest you employ a canonical tag on your pages and that you tell GWT that the parameter does not change page content. I think the AWeber link tracking can be disabled, as can the tracking of most other services.