Knowledge, experience, and attitude are the most valuable assets you can have when it comes to being self sufficient. However, owning some equipment or stocking up on some supplies can speed up the process and makes things a lot more enjoyable for you.
This list is a live document and I will make additions from time to time.
Here are some good lists of equipment, tools, and other supplies that I have found online:
Intermediate Information on a Basic Tool Kit Part 1 / Tool Kit Part 2