AdWords suggestion too can be quite skewed.
Big +1. Having said that, still a vital tool to be used.
As link8r mentioned, it's about taking an holistic approach and utilising as much of the data you have available as possible. Along with the various tools, don't forget the simple (but very important) steps of listening to how customers talk about the product/service, watching/analyzing what they say in mails, using your analytics to monitor on-site search, etc. etc.
Not quite 'analysis', but something that you'll be considering as part of your kw research is the related terms. There are various ways to help identify what terms the search engines deem as semantically related, for example using the "~keyword" search query on google (and observing the bolded results) or using the
wonder wheel.