The crafting skills in Star Wars: The Old Republic require components earned from Crew Skills missions:
Pay 97c, send Khem Val away for 3 minutes, and poof, 2 Rubat Crystals (or whatever).
Do I have to do Crew Skills missions to get profession reagents, or are there other (less "pay credits + give up your companion") ways to do so?
This depends on the Crew Skill.
Gathering skills, (i.e. Scavenging, Slicing, Bioanalysis and Archaeology) all have nodes scattered around various planets which can be gathered from, as in other MMO's.
Mission skills (i.e. Diplomacy, Investigation, Treasure Hunting and Underworld Trading) do not. The only way to use them is with missions.
In general, even with Gathering skills, sending your spare crew members on missions will result in a much better yield of materials, along with being able to target the specific mats you need without entering zoned which you cannot handle or which are trivial to you.
