This will be a living list of tools and will grow over time. If you have suggestions, please drop them in the comments and I will get them incorporated as time permits.
Some tools will be noted as “No Touch”. These are tools that you can use with little to no chance of your target knowing that you are looking into them. This is good to know at times. I will have to write a page that goes into more depth on the No Touch concept.
MXToolbox This is a collection of tools that you can use to gather information about a domain, email server, etc. It is a very common tool when I am researching. This may be No Touch as the traffic would not point to you.