Younger girls these days speak with a lot of vocal fry, or giving their voice a creaky-croaky delivery. See this previous post to get a better description, examples from YouTube, and an explanation of why it signals social avoidance. (And thus, the rise in avoidant personalities has caused a rise in the use of vocal fry.)
All commentators mention that this vocal register became famous with the singing styles of Britney Spears and Kesha. But it must have gotten started gradually before them. If it does track social avoidance, it probably would've gotten started around the early '90s. You wouldn't hear it much, perhaps not at all, in songs from the '70s or '80s.
I've found two examples that pre-date Britney Spears by awhile, both released in 1995: "Who Will Save Your Soul" by Jewel, recorded in '94, which has vocal fry in many spots of the verses; and Marilyn Manson's cover of "Sweet Dreams (Are Made of This)", recorded in '94-'95, which also has pretty extensive vocal fry. The Manson song was more of a caricatured voice, didn't climb as high up the charts (though it was popular), and is by a male. So you might call that one a little unrepresentative, though it still is there, years before Britney Spears and more than a decade before Kesha.
The Jewel song is more relevant -- by a girl, not in a context of caricature, and delivering world-weary lyrics about only trusting and relying on yourself. And that song was on the radio and MTV non-fucking-stop.
I couldn't think of these off the top of my head, but followed some hunches by reading through the Billboard Year-End Singles chart (here is 1995, with other years at the bottom). If you remember the singer projecting a kind of cocooning, through-with-boys, or other jaded kind of attitude, that's probably worth looking at. If it's clingy or needy, it won't have vocal fry, since she's trying to get him to come closer, not push him away. That clingy-needy song "Stay" by Lisa Loeb, for instance, has no vocal fry.
Browse through that Billboard list if you're up for it, and let us know if there are other examples of persistent vocal fry in pop music before Kesha and Britney Spears.
Fucking Jewel, I knew I didn't like something about her, right when that song came out. That whole "I'm too scarred and wounded to let boys get close anymore" vibe that she put out. But girls who have creaky-croaky voices are avoidant and never let boys get close in the first place -- that too-wounded thing is a total facade.