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G webmaster central + G analytics
Google adwords keyword tool
Seobook keyword tool
Yahoo site explorer
Link diagnosis / backlinkwatch/domain pop
G advanced search operators
Web developer toolbar
seoquake / quirk search status addon
hubfinder from seobook
If you have more money to splurge:
Eyes / brain / analytical mindset to extract actionable insights from data given by tools
Hope this gets you started.
And they were:
Keyword research tools - free from most search engines and there are some excellent paid subscription ones too.
Analytics software (lots of options out there both free and paid) - so you can actually see what is happening. So much better than chasing rankings, chase converting traffic! I haven't checked ranks in over 7 years for anything anywhere. There is no need, analytics tells you what words are ranking, how effective that ranking is and how effective in getting conversions those words are!
Checking for backlinks - again, you can do that via search engines for free or there are tools to use.
Apart from that, there is really no overwhelming piece of general technology for SEO that I can think of that you need to do your job.
I could, of course, stand to be corrected!