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.

I really liked the dice game from The Witcher.

I became strangely addicted to it. Along with Caravan in FO:NV

I think the OP is looking more for Mini'Challenges rather than Mini Games, which is cool.

However Mini Games in and of themselves have always bugged me as it takes the game away from the PC's Skills and Attributes and puts the outcome almost totally in the skills of the person playing the game. That is not Role Playing.

So, mini challenges I can get behind, but not for Lock Picking, Conversations, and other in game interactions that are or should be based on a skill or set of skills.

I feel like they labeled lock picking and conversation in oblivion as a minigame to make them appear more fun (i.e. look!!! even our lockpicking is a game now!!!), when in reality they aren't really games at all, just rituals you must do to open a lock or make someone like you.

As I said last year, (hehe), I want minigames! Anything to spice the feeling of Skyrim up a bit. Maybe if you'd reload your previous save, the person you waged against would call you a cheater and refuse to play, or even start a 1 vs 1 fists only brawl with you!

As long as there not the ones like Lockpick,speechcraft type were you have to do it over and over again through out the game then I have no issue with it, I used to like all the mini games in the Final Fantasy games, FF7 even had an indoor amusemant park, that was fun, but it was not apart of base game mechanics like the lockpick crap form OB.

Like it or not these "rituals" are referred to as "mini-games" in all games now.

Absolutely not.

For one, they do not belong in an RPG, where success should rely on character skill, not real life button pushing skill.

Secondly, I have never ever seen a mini game in any game that was not lame.
They always seem to be 1980's atari console games ported straight in. And I already thought the atari was lame in the 80's.

The very best minigame I have ever seen was simply an arcade machine in a bar, where you could play space invaders on.
And Ive played that exactly once.