Of the guns I own, I never even considered barrel twist and how would I determine what they are? Are the higher twist rates a modern phenomenon? If I purchased a gun 30 years ago is it likely that the twist rate is 13 or 14?
Rifling is used to impart spin onto the bullet so as to maintain gyroscopic stability. ...like throwing a nice spiral football pass.
If the spin is too slow, imperfections in the bullet will lead to inaccuracies or even tumbling.
If it's too fast, then the bullet won't travel optimally either and impact may not be perfectly head on, but it's usually better to spin a bit too fast than too slow.
Over the last few decades significant improvements in bullet construction, powders, optics, laser range finders, ballistics software, etc... have led to a lot more bullet choices in the long, heavy, VLD, boat tail designs with much improved BCs for better long range accuracy especially in windy conditions.
Previously, the long bullets may not have held together when spun at the required twist rate/velocity. This can still be a problem today with the longest bullets and biggest magnums. In extreme cases, you can shred the jacket as it leaves the barrel.
So, yes. There has been a trend towards slightly faster twist rates even in some factory barrels. But, especially in aftermarket custom barrels.
Most modern factory barrels will shoot a wide range of bullets. But, the "heavy for caliber" bullets often require a faster twist than the average factory barrel.
You can measure your twist rate. There are articles and threads here explaining. Barrel mfgs often post guidelines on twist rates for calibers. And, JBM Ballistics has a website for calculating stability. If you still need help, post a thread and someone will explain.
Hope this helps!
Richard