I'll start with one:

Secret of Mana:
This game plays like an action game in which you manually control your character and press the attack button to swing your weapon. However, when your weapon collides with the enemy, it doesn't just automatically hit; that would be too simple. Instead, the game randomly decides whether the collision was actually a hit, and if not, your weapon just passes through the enemy without doing anything. (In a turn-based RPG, this is common, but in an action game, it just feels strange.) Note that this also goes for enemies attacking you.

Also, spellcasting is also bizarre; to cast a spell, you pause the game, select the spell and target from the menu, and the spell is then cast. Honestly, I think this game's predecessor, Final Fantasy Adventure, handled spellcating better; you equip the spell and press the spell button to cast it there; makes much more sense in an action game.

Secret of Evermore:
Like Secret of Mana, but one difference: If your attack collides with the enemy, but the game decides the attack doesn't hit, the word "miss" appears over the enemy. In other words, you can charge up your spear, aim it, and throw it at the enemy, have the spear collide with the enemy, and have the word "miss" appear over the enemy. Does this make sense? (Spellcasting is like in Secret of Mana, though the limiting factor on its use is different.)

Any that you can think of?

Good ol' Morrowind does this too. I wish you happy flailing whilst leveling those low level melee skills. Not at the moment but maybe something will spring to mind.

Not a mechanics per se, but when I was watching some Persona 3 videos on youtube, I found them to be quite disturbing.

I mean, characters shoot themselves in the head to call on Persona powers in combat. One heroine shoots herself in the mouth... And you see this several times a turn.

Slightly similar, but straightforward mechanic is in Final Fantasy Type-0. Characters summon Eidolons at the cost of their lives, which is heavy price to pay in comparison with other FF games.

Final Fantasy 8 was a game filled with poor choices: Want that new spell? Spend the next 5-10 minutes drawing it. Want to use it? Well hope you haven't bound it to a stat or you'll be nerfing yourself every time you use it. Want to collect all the cards? Well you have to loose some of your most valuable cards at a certain point to a certain opponent–but don't worry– you'll be able to win them back in a few dozen hours when you meet another character, provided you choose to play cards with them. Oh, we won't tell you who or when, not unless you buy our guide. Feel like exploring the city? You're wasting time doing un-SEED-like things, so you'll be demoted. Etc.

Does an entire control scheme count? Because the hit or miss of Skyward Sword's Wii Motion Minus controls is something to behold.

Trespasser's wacky one armed gameplay.

SNES -> Magna Braban: Henreki no Yusha (Japanese-only release)

Its combat system is weird. Watch gameplay videos on YouTube.

Endorfun had a pretty weird mechanic (which was the game). It was a puzzle game where you controlled a cube with a different color on each face. Each level was a grid with colored squares on it. The objective was to remove all the colored squares, which you did by rolling the cube over them in such a way that the color on the upper face of the cube matched the color on the square.

Anal Probing in Destroy All Humans to get DNA to upgrade the main alien character Crypto.

I do not need to explain much more beyond that statement.

Controlling two characters at the same time:
Never Alone, the titles is well chosen for this one, you should never play this alone...I did. Also, I keep getting flashbacks of me failing in Never Alone whenever I play something similar like Brothers - A Tale of Two Sons.

I recall in the first Baldur's Gate the combat would get unpaused if you went to the inventory view.

I don't know if that was supposed to be realistic or why it was like that, but it irritated me anyway. I think they changed that for later games (BG2? IWD?), ie. combat would stay paused even when you are in the inventory view. I was going to mention that too.

Final Fantasy is an odd series that each game seemed to reinvent the wheel, just for the sake of reinventing it. A new FF game would have an overhauled magic system. Not necessarily better or worse, just different (in the case of FF8, yeah it was worse...). You needed to re-learn the magic system each time.

On the other hand, combat (non-magic) seemed more evolutionary than revolutionary, just like you'd expect it.

The Katamari games have pretty absurd gameplay mechanics...I mean, the whole game is rolling around the game area collecting stuff lying about to increase the size of your rolling ball.

SaGa 1 has some strange mechanics that are most likely due to bugs. For example:

When a basic STR-based attack is used, AGI is halved for the to-hit calculation *unless* the attacker or target is blind. In other words, being blind increases the character's accuracy with and evasion against STR-based attacks.

Multi-hit attacks do extra damage equal to the target's AGI with each hit. However, the attack has to hit in the first place, so high AGI can prevent the attack from hitting, but will increase the damage if it does hit.

Group attack spells, when hitting a party member, do less damage if the target has high MANA (unless the target is weak against the attack). This does not happen if the target is an enemy group.

If an all enemy attack is used on a target weak against it, it does less damage based on the target's MANA. (In other words, being weak against the attack reduces the damage you take.)

The MELT attack of slimes, as well as the DRINK attack, will do more damage if the target has higher MANA.

SAW is more likely to work if the attacker has higher STR. *However*, *unless* the attacker's STR is *less* than the target's DEF, the attack has no chance of working. (At 100 STR, there are only 2 enemies that can be instant killed this way; one isn't supposed to be killable, and the other is the final boss. At least it's guaranteed to work on those two targets.)

Espers (Mutants in FFL) may gain stats or new abilities after battle. This is determined by an RNG that is quite terrible; it gives the same random number sequence after the game is turned on.

After each load, combat will use the same sequence of random numbers. This means that if you load a save, fight a boss, get unlucky and lose, reload the save, and then fight the boss the same way, you will get unlucky in precisely the same way. This can occasionally make it necessary to manipulate luck in order to win a fight.

System Shock 2. In a world where they can make starships, but not guns that can shoot for more than 10 minutes without wearing out. The epitome of "lets put something in the game just so we can have an RPG skill to counter it". Seriously, real guns can easily go for a year and still work. There is no place for weapon wear in the time scale of most games.

Also System Shock 2. Lets set the difficulty by using a totally unrealistic respawn rate. You could walk out a door to a dead end, closed off area, walk back through the door and watch the same enemy literally just zap into existence right in front of your eyes from out of thin air. Lazy dev work that almost borders on developer cheating. Shit game.