Ubersuggest Keyword Research Tool
Ubersuggest is a tool that scrapes Google Suggest. Google Suggest is the feature that gives you suggestions on what to look for as you type your search in the search box. These suggestions are based on existing Google content and search behaviors of Google users. So you can find actual search behaviors for which you can optimize your website.
It does not help you see what people searched for to get to your site, but can give you an indication of what concepts and keywords may be worth investing in.