I once wrote a small script (in C#) to pick a few tens out of a few 1000s. I got weird repeats. I switched to a cryptographically secure RNG, and the repeats were gone. It was probably pure chance, but I stopped using the normal random function ever since ;)

The new Baldur's Gate game has a setting called "karmic dice", where it apparently biases the dice rolls to not cause repeated outcomes as much (i.e. if you're passing checks a lot, it will start to bias towards lower results, and if you're failing checks a lot, it will start to bias towards higher results). They devs made the interesting decision to have that setting on by default, which I'm guessing is based on the experience they expect more players to want. Regardless of my own preference, I think it's pretty cool they made that an explicit setting that players can choose to keep on or turn off.

I was once tasked with creating a DVD game that was meant to randomly pick questions from its available pool. Learned lots of things about how unrandom random can be. On the lower end of DVD players, there was a stored list of values between 0 and maxInt that was randomized when created. Each call of the random function would just move the pointer to the next item in the list. This meant that it would essentially play the questions in the same order every time. I can't remember the specifics if the list was reset when loading a disc or when the player was turned on.

Turns out, the company wanting the game got scarred of some patent that invoked the word random, so we had to reprogram the thing essentially do the same as that player. We had multiple sequences of randomized questions, and the game pick one of the sequences to play back in order when started.