I've been coming across keyword research posts now and then and decided to make up an extended list of the tools which appeared particularly useful for me.

1) Google Adwords Tool for keyword suggestions (well, this one is used by everyone here, so it does not require a long explanation). I always have "Show synonyms" ticked to get more ideas, and I also like to play with sorting options. (To get keyword suggestions and all the possible info on them, I also often turn SEOBook's wonderful all-in-one keyword research tool.)

2) More synonyms from Google:  Google Sets. This one not only allows you to get more ideas to expand your keyword list, it also shows what G considers relevant (if you, for example, care to find more anchor text variations or trying to create a most relevant text around your link).

3) Misspellings. Honestly, I've never used it. If you have, please share your experience on how it can help.

4) Find your keyword associations by searching eBay (a huge thanks to Linda Bustos for this great idea). Define your PPC campaign negative keywords. Besides, if you are creating your brand name, make sure it has no negative or fixed positive associations (which, in both cases, could be rather hard for you to brand in both cases).

5) Define your targeted audience with MSN Demographics Prediction tool (also not very often used by me).

6) Google Trends. Ok, I will have to describe it in a bit more detail because I've had some positive experience with it recently. I've been doing keyword research for a client of mine who owns a pretty directory of auto insurance companies. The first issue he asked me to explore was the distinction between 'car insurance' and 'auto insurance', so I decided to go ahead and compare these two in Google Trends (an awesome feature, by the way!):

The search for 'car insurance' seems to dominate. But Google news search seems to love 'auto insurance' more. I went further and limited my search to US only: 

The discrepancy occurred due to US results - Google News Search is definitely biased to US news. To target the US public it is better to go with 'auto insurance', while for the UK 'car insurance' is more correct. To sum up this long story, these are the two most useful features of Google Trends: (1) it allows to compare two [similar] queries, and (2) it allows to define where the two keyword sets are most popular (and, if you need it, when).

More reading on keyword tools:

SEO & PPC Competitive Analysis & Keyword Research Tools

Advanced Keyword Research — The power of understanding your visitors