The list of potential non-combat skills can be found here. This is not meant to be an exhaustive list, and if you have a skill that you believe would fit in to the world of Thedas, by all means, ask the moderators!
There is no limit to the number of skills that a character can have, but they must be supported by the background and history. A simple soldier in the Bannorn would not be expected to have an extensive familiarity of Nevarran Heraldry, for example (unless perhaps his mother was exiled Nevarran nobility, also as example).
Civilians are the artisans, the crafters, the tavernkeepers, the musicians, the workers. They would be expected to have a higher proportion of noncombat skills tied to their chosen professions.
Non-combat skills that a typical mage might be familiar with include:
- Arcane Lore
- Religious Lore (Chantry mage only)
Other skills may be suggested by their background. A Circle mage, a Dalish Keeper and an apostate born and raised in Denerim will have very different skill sets.
Non-combat skills that a typical rogue might be familiar with include:
As with the mage class, a character's background will suggest the appropriate skills. A pickpocket living on the streets of Val Royeaux will differ from a Bard moving through the houses of the nobility.
Non-combat skills that a typical warrior might be familiar with include:
- Military Lore
Once again, a character's background will inform your choices. A common mercenary might not have the same skill at leadership or military lore that the captain of a noble's guard would possess.
Fleshing Out Your Character
None of the skills listed above are restricted to the classes that they are associated with. Want a city elf apostate who can pick pockets? Go for it! A thief with strong leadership skills heading up a gang? No problem! A warrior who knows how to pick locks and disarm traps? Absolutely!
Beyond that, all non-combat skills are open to all characters. All that is required is for the skill to fit logically with a character's background, so let your imagination go. What skills was your character exposed to in their childhood? What are their hobbies? It's the little details that can really make a character come to life and be fun to play with.
Proficiency in existing skills and new skills may be gained through roleplay. Characters may learn a skill from other characters if the proficiency of the teacher is higher than that of the student.