Keyword research is the basis for a successful web creation, web business, search engine optimization (SEO). I will list free or freemium (free plus premium tools) tools that I have tested.
Google has a free keyword research tool. For some really hardcore niche terms, it does not give as detailed of info as some other paid services but it gives a general idea as to relevant keywords or phrases.
For example, I wanted to test relevant keyword for the word 'hanryu' (Korean wave). Google keyword AdWords tool listed relevant keywords / keyword phrases that otherwise I would not have known about (such as 'Korean wave actresses', 'hanlyu' (different spelling)).
I divided the Google keyword research between localized (Korea) setting and global setting. The local research for the term 'hanryu' returned 3 results (showing me there were not many natives looking up for that term in English) whereas the global result returned a whole list of relevant keywords and phrases that I could utilize were I to create a site dedicated to that niche area.
Wordtracker
Wordtracker: There is a 7 day free trial option or you can test it out a few times for free without signing up. Their instructional videos are extremely helpful in understanding basic concepts of keyword research, finding niche terms and understanding SEO among other topics. Wordtracker is a neat tool for analyzing keywords, creating strategies with their tools and for link building.
Unlike Google's tool (which gives monthly volumes), Wordtracker gives a daily volume count. If a beginner, and interested in understanding more about keyword research, SEO and internet marketing in general, Wordtracker is a good start.
Keyword discovery
Keyword discovery is a great tool to understand a rough estimate of search engine percentage of traffic related to a certain keyword. For example, if I type in hanryu, it gives ms a chart showing me that there are more yahoo users looking up for that niche term. It is a great way if doing PPC campaigns to find out where to focus on instead of just going for google.
While it does not give as great of relevant keyword terms or phrases, I found the search engine traffic estimator to be extremely useful.
If unsure of the product, it can be tested for free without signing up.
Wordstream
Wordstream is an extremely comprehensive research tool with a neat niche area column that helps keyword researchers narrow down what term to use for the niche.
If accessing the site from the same IP address, it limits the free research to a few times but still worth looking into it at the initial research stage.
Wordstream is more fit for those looking into PPC campaigns or for agencies looking into a large keyword database.