Interesting question. My first reaction was "we don't need no steenkin' tools.." but then I thought "don't I - what outside technology do I actually use.."
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!