Yes if not skill related, like speechcraft minigame of oblivion.
Something like this:
- You can challenge people to race with you to a destination, by any means.
- You can join a local village contest to do a simple task, and a reward for the winner.
- Duels with other people, like blade to blade, or spell to spell.
- Like "Conan the Barbarian", join full contact local fights in each settling, and win the tournaments.
- Offer to teach a skill to a person for a price, and spar with him for a while.
- A kind of table top game, regular in Skyrim taverns.
- A very special minigame which I will describe here:
There can be a minigame which is kinda interesting.
There can be special randomly generated/populated complex dungeons/caverns, full of hostile opponents and traps, scaled to difficulty level of the contest, and some people offer to join the contest, and the winner is rewarded, by an item scaled to the difficulty of the contest.
Each contestant wears a simple rag cloth, and is allowed to use a basic weapon/offensive spell, and starts in a random place inside the dungeon, and the goal is to remain the only alive/conscious contestant after a while, so you can actively seek and kill/disable the other contestants, or try to lead them to traps/opponents, and you can seek and find better equipment for the task, or learn about the traps and how they can be useful for your goal, and so on...
If you can eliminate all the other contestants while avoiding/removing local hostile elements, and be the last surviving one, then you are released from the dungeon. Your new equipment/learned spells is replaced with your original ones, before the contest, and you are awarded with a new item/spell or gold of your choice, scaled to the difficulty level of the contest.
You can start with easier contests, and move up to become the champion of it all.