New Game Mechanics

Most mechanics are recycled over and over. And the games are almost always different combinations of these mechanics.

A new mechanic is hard to think of. And only by sheer luck, you might think of a new one.

Either you combine existing mechanics and you think of a way to replace them by one new mechanic.
Or you think of an entirely new mechanic in the first place.
Either way, I think it would be a waste to discard the mechanic if you see no choice, without sharing it with the others. You even might find out that it already existed too.

I have one mechanic, that I am 100% sure of being unique. I design all my games around this mechanic. But it is my hobby, so don't think much of it.

I'm not trying to invent any new mechanics, but I am looking for interesting mechanics to support my theme and the flavor of my game.

You have to define mechanic though. The definition I like to work with is from the Critical Gaming Network: "Player initiated actions from controller inputs as designated by the game designers. These actions have effects on the gamestate in terms of the variables and dynamics of the gameplay system." That really applies to video games, and frequently I've heard e-sports commentators and shout-casters refer to a pro-player's "mechanics" in this manner.

So common mechanics, using this definition would be rolling dice, playing cards, pulling or placing tokens, meeples, or chits, turning a card a certain number of degrees, moving any of the above around, etc.

It would probably be easier to design a new "rules system" than think of a new mechanic. For example, Dominion was hailed as the grand-father of the deck-building genre, but all it did was take a common mechanic (drawing and playing cards) and change the setup and rules surrounding a players deck.

However, you can really think outside the box. The role-playing game Dread uses a Jenga tower as it's primary gameplay mechanic, as each action a player attempts requires them to pull a block from the tower. Each pulled block makes the tower more precarious, which is thematically consistent with the rising tension (i.e. dread) within the story being told.

You probably don't want your gameplay to be primarily dexterity based though. For example, a game mechanic could be balancing an object on the back of your hand, or, as was the case in early Magic: the Gathering, dropping a game object from a certain height above the table. (Whatever cards it touched were the cards effected.) Those are all interesting mechanics in my opinion, but they aren't exactly great in their respective context.

The mechanic that interests me currently, is players manipulating hidden information on the table. Placing cards face-down, and being required to check your opponent's face-down cards (a la Android: NetRunner) is a great mechanic in my opinion.

While games often try to simulate an imaginary contest through mechanics (as in LOS's point 1), there is some value in finding a unifying theme for the mechanics or components in a particular game.

The Rolemaster system came up with a bazillion different ways to use 2d10, Monopoly does almost all of its state-recording with slips of paper/card, etc.

So once you've identified the core Thing you want your players to do each turn, each new thing you add should be weighed against the added cost of additional components and whether it fits in with the other stuff you have players doing. This means the peripheral elements of your simulation will have lower fidelity (using a not-quite-optimal mechanic), but that's better than detracting from the core.

It's fine to have a couple different aesthetics going on, for example, pawns physically placed on the map and some kind of status track... but you don't want to go crazy with half a dozen unrelated systems.