Google operators can be one of your greatest allies in link research. You can get a listing of the major links to any given page or website simply by searching link: url. While it is good to know what backlinks to your own website exist, this information is especially useful when researching your competition. If you know your competitor is coming up earlier in search engine results, looking at their incoming links may provide perspective as to how their gained this preference. You can then court the same or similar websites to get your own solid link base.
Once you have a list of who is linking to your website as well as the competition, you can search for the keywords that make these linking domains relevant and authoritative. This may give you inspiration for other sites where backlinks may be possible. This is as simple as googling site: url keyword.