Life imitates art.

Criminals are apparently the original source of the popularity of burner phones. As a page on the web site of Pure TalkUSA, a "nationwide provider of low cost cell phone plans with no contract", explains:
Burner phones came to fame with the television show "The Wire," when drug dealers used the phones to communicate. However, these devices have been criminals' go-to long before HBO made them famous.

Since prepaid phones can be bought with cash (and without a contract), they’re much harder to track. So it's easy for people to use them for certain (illegal) activities and then simply dump the phone—and more importantly, the phone number—when it’s considered "burned," or too risky to use. Then, these users simply buy another pay as you go device.
But that "coming to fame" reference suggests a chicken or egg question of whether the screenwriters got the burner phone idea from the criminals, or whether the criminals picked up on it from the screenwriters. I don't know to what an extent criminals watch television, but it seems to me entirely possible that seeing burner phones used on crime shows could convince them that they're a good idea. On the other hand, if they do watch a lot of television they've probably already have figured out that our fearless law enforcement services are even capable of tracing those untraceable burner phone calls.

Go to: Common knowledge, or
Go to: Ain't no need to hide, ain't no need to run.