1. Food Production
Food production will be a hugely important skill in a long term collapse, and it's something that few people are skilled in these days. Even people who make a living through farming today will have a tough transition to a world with limited fuel-powered tractors, pesticides and so on. Knowledge and skills in food production--things like gardening, raising livestock, hydroponics, aquaponics, traditional farming techniques and related skills--will be hugely important to keeping communities fed and alive after a large-scale collapse. Knowledge is very portable, as are seeds.
Hand sewing and the ability to repair and make a wide variety of things would be quite valuable. While the average person can probably sew a hole in their pants, can the sew up a backpack, chest rig, pants, tent, sleeping bag, shirt or similar? Probably not. As pre-collapse goods wear out and disappear, sewn goods will become very valuable. A sewing kit and associated tools is quite light weight, and cloth can be scavenged or bartered for. Though less mobile, a treadle/foot powered sewing machine would make life a lot easier.
3. Community Defense
The average American has little experience with weapons and defense, and when there's mobs of potential enemies roving the lands, those who do will find their services in high demand. Whether it's serving as a guard or defender, or helping train and prepare a community defense force for troubled times, people with skills in this area will have an easier time finding a place in a post-collapse world. Defensive weaponry, a trustworthy appearance and credentials would help.
Demand for medical services will skyrocket in a more dangerous, accident-prone post-collapse world. The traveling doctor, making house calls on patients, would see a resurgence. Formal training/credentials would be important, as would the appropriate equipment, and probably also a sound knowledge of natural remedies. Very valuable and likely to help keep you alive in many circumstances.
5. Radio Operator
HAM Radio operators are not exactly common these days, but they could be a source of information and communications with the outside world. A portable, solar-powered HAM set up and knowledge of communications tech would make a survivor a handy person to have around in troubled times. Access to information and the ability to send messages over a long distance would put your services in high demand.
There's five professions--I'll post up 5 more next week. To those interested, I'm sure my seasoned survival readers will have plenty of other ideas in the comments section,