From my limited experience, generally, if they're still green, they're still good to eat. However, the more mature they are, the thicker the skins may be and the more well-developed the seeds may be.
Some varieties seem to taste fine even after yellowing to ripeness, though (e.g. Monika), while some are extremely bitter. The soil may affect how fast and if they get bitter, too. It's possible that still-green cucumbers may get bitter if they are mature enough, but I think the variety and soil conditions have a lot of influence here.
To illustrate this, I had a friend in my county who grew awesomely huge, green cucumbers that were likely of the Bushy variety. She gave me one, and it tasted excellent. I saved the seeds and planted them the next year. They only produced small cucumbers, and if I left them on the vine a long time to yellow, they were extremely bitter. (I attribute the difference in size and flavor mostly to the soil.) The Jolly Green F1 cucumbers I grew along side them were not so bitter.
In 2016, I grew Monika and Beit Alpha (among others), and neither of them had bitterness issues. Beit Alpha never turned yellow, though, but Monika eventually did, and still tasted great. Both Beit Alpha and Monika outperformed Bushy and Jolly Green F1 considerably, too, but I did water them differently. EDIT: While Beit Alpha never got bitter, I should note that really old fruits I tasted later in 2016 tasted like lemon cleaner smells (but they weren't bitter, and the lemon taste made them great for new culinary purposes). I think the lemon taste is the plant's reaction to anthracnose trying to make the fruit rot; the lemon-tasting stuff may be in order to fight the pathogen. That's just a hypothesis, though. But, there was anthracnose trying to infect at at least some of them (but it never went deeper than the skin in 2016).
Leaving fruit on vine longer often does mean the plant will produce less fruit than if you pick them sooner, with many, if not most, plants.