Here's a quick overview of the free keyword suggestion tools on the market;
Overture Keyword Assistant - UK.overture.com
Probably the most well known tool around. Unfortunately due to the high volume of usage this tool moves as slow as a slug. Although fairly useful the data provided is only relevant to the number of searches conducted on the Yahoo! engine. It also has 'singular' and 'plural' issues in that it may provide volumes for 'cheap flight' but not 'cheap flights'.
Google AdWords Keyword Tool - https://adwords.google.co.uk/select/KeywordToolExternal
Google's tool is more widely used for Paid Search (PPC) campaigns, but is useful to inform keyword selections for an organic search campaign. This tool will provide rough search volumes, and even search trends but will not provide exact figures on the number of searches conducted on Google.
Like the Overture keyword suggestion tool, the Google Keyword Tool can be used across many different markets and languages. It can even analyse the keywords used across a particular site.
Wordtracker - http://freekeywords.wordtracker.com/
This was a new tool unveiled by Wordtracker earlier this week. Wordtracker are famous for having a paid-for keyword suggestion tool, so it was nice to see them provide a free tool.
Similar to the Overture keyword suggestion tool in terms of layout, Wordtracker uses a specific formula to track the estimated daily search volume of keywords. More information on their methodology can be found here.
KeywordDiscovery (Trellian) - http://www.keyworddiscovery.com/search.html
Last but not least KeywordDiscovery have launched their free version of a keyword suggestion tool this week. The main Trellian tool is popular across the pond and this tool is possibly my favourite of the three.
KeywordDiscovery generates the top 100 keywords from data collected from across 180 search engines worldwide, providing a more global slant on its results.
The main Trellian keyword suggestion tool also organises keywords into industry specific categories - very useful but requires a subscription.