These are the tools that I use on a regular basis. Checking backlinks is very important. Find out where your competition is listed and then try to get similar links. It is also good to know where you have backlinks..
Ahrefs - View your backlinks, or the backlinks of the competition. This is the best tool that I could find.
SERP Book - If you have more than 5 websites reviewing search engine rankings can become tiresome and is not time efficient. Access all of your rankings for all of your websites in one place.
Google Keyword Tool - Analyze which keywords are worth targeting