Timers are cancer and boggle down exploration,they make people wonder if other quests are also timed,thu making you paranoid.
Good timed quests give you a proper warning about being timed rather than just randomly dropping a time limit on you.
As? Examples needed. Mixing timed quests in normal rpg is stupid. Kingdom come did well,because the whole world was kind of progressing or gave that illusion. It was more of a medieval simulator than anything else. So having a game focused on realism would have timed quests.
Still there are a few variations of timed quests,some are time in way you could take them only at certain in game time (those are the worst),also there are ones that are takeable whenever but do have time to complete it. I am yet to see a game that does it well,some of them like KC do it passable,but not good. I like exploring at my own leisure and hate to rushed. If i wanted that i would have gone to work. Developers do tend to add that shit as a gimmick,to diversify the gameplay.
No existing RPGs that do it well come to mind, but it can work out well enough, especially if you modify the results of the quest instead of making it a hard failure, and making the time limit generous enough.
Example: a woman who's being sold at the slave market asks you to buy her and help her out, because she's a noblewoman who was betrayed and sold into slavery. She wants you, a capable adventurer, to help her back to her estate.
If you don't buy her right away because of a lack of money and return, say, a week later, it turns out she was sold to someone else. You can ask the trader who bought her, visit that guy, and buy her off his hands for a slightly higher price.
Not a big drawback for taking your time, but it shows that the world isn't just waiting for you.
Other example: a guy wants you to find his missing wife, who he suspects was abducted by evil cultists who want to use her as a human sacrifice. If you find the cultist lair in time, you'll find her in a cage and can free her after fighting the cultists. If you take too long, you'll only find her dead body on the altar.
Etc.
In those hypothetical cases, you won't fail the quest if you take too long, but the quest will turn out differently.