Many folks out there have some food, a sustainable garden plot, a water source and no clue. They refuse to consider the position they will be in if they are forced to use their resources in an environment where there is no rule of law or modern convenience. Sometimes the best laid plans can be thwarted by a seemingly innocuous incident or situation. The skills discussed will help hedge your bets and make you a more rounded and valuable person.
Medical training is my #1 skill set to have training in. Without 911 or modern surgery procedures, even a modest education in the medical field can save you a lot of heartache later. Dentistry is included in this skill. There are many resources that you can purchase to help you along and get you up to speed if we face a severe breakdown in society. You may ask yourself why you would need this skill, because ambulances didn't run to the riots in Fergadishu.
Agriculture/forestry- Learn how to spot problems and how to care for our natural bounty.
Animal husbandry- Because healthy animals are tasty.
Blacksmithing- Without modern machining techniques, parts will have to be hand made and this is the least expensive and easiest way to make parts.
Electrical/electronics/comms/solar- Information is key. Weather can be predicted by outlying broadcasters. Threats and conditions can be broadcast. Solar power is useless without the knowledge on it's use and delivery systems.
Plumbing/sanitation- Disease and poor sanitation killed more people than bullets did during the last civil war.
Mechanical skills/ light machine work/gunsmithing- Fixing your own stuff becomes more important when you can't call someone to fix it for you.
Carpentry/roofing- Keeping your home dry and being able to modify it to fit your needs will be important during a crisis.
Textiles/sewing. Clothes won't come from India or Bangladesh anymore. You'll need to make/repair what you have.
This list isn't comprehensive, but it's a start. Learned skills and education are 2 things that can never be stolen from you.