My 2c : AdWords suggestion too can be quite skewed. I blogged recently about "Fine Fail" - the Makey-uppy party that Google AdWords suggested receives more searches than any other - yet the phrase couldn't possibly. There are quite a lot of sites like compete.com and wordtracker that need to form part of a holistic approach.
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.
I tend to use Google Keyword Tool as its easy to find haha but theres many out there and they all show slightly different results so it can be interesting to used a few to find a safe bet of a good keyword, its the old don't put all your eggs in one basket scenario
I concur, I recently did some research for a client and lets just say the term was SEO Expert, the plural (SEO Expert'S') showed zero local searches, versus several hundred for the singular version 'Expert'. Sorry Google - I just don't buy those results.