Here are a few of the tools that I actively use in my marketing. I'm including both free and paid tools (I'll identify which are which), but I'm only listing those that I actually use myself. It's entirely possible that there are other competing products (in most cases there are), and some of them might be better, but these are what I work with.
Keyword Research Tools
Google Keyword Tool (AdWords) - This is my go-to tool for quick and dirty. It's the first result for 'keyword tool' or 'google keyword' or anything similar, so I don't even have to remember a URL. I can get a super fast answer to high level questions. Great for finger-in-the-wind type research.
Micro Niche Finder - This is the tool I use for more in depth keyword analysis, or for larger scale research. It's a paid tool (one time fee). It uses data from the Google Keyword Tool as a base, but folds in data from other tools. In addition to information on number of searches, it can also give you number of competing sites, strength of competition, readiness to purchase, etc. It also saves all your searches for easy access later. I like it because it let's me get a group of keywords together and then sort them by how hard/easy it will be to rank for them.
Backlink Building Tools
Free Traffic System - I just recently started using this free service. They have a network of opt-in blogs which you can publish your articles to. Each article you publish can be published on up to 30 different blogs (more if you have a paid account), each with two links of your own. They spread the links out over a few days so they don't all pop in at once, and you can spin your content, links, keywords, titles, etc, if you want. As I mentioned they do have some kind of premium/paid account, but the free one offers plenty of value.
Other Marketing Tools
Traffic Travis - I picked this free desktop tool up a whlie ago and still am only taking advantage of a few features. It has a nice checker tool that will do on-page SEO analysis, pointing out the big/obvious things that you should have caught but maybe didn't. I also use it to keep track of how my sites are ranking for my focus keywords. It has some basic keyword research capabilities but it didn't seem robust enough to me. I believe they have a paid version, but I'm not even sure what it does or what you gain.