One of my favorite things to have happen in videogames is for the game's story to make reference to a choice I made earlier in the game. It's a simple enough thing, but it lets me know that the game cared enough to pay attention. It's also one of the reasons that Telltale Games' games have that "X will remember that" as an indicator that a player made a choice. The thing is, one of the earliest choices players often make in games is who their character was before the game, and that choice should matter too. Even if you don't want to work your whole plot around the PC backstories you can make it matter. Your players cared enough to make it. You should care enough to at least acknowledge it.
The first way I've seen GMs reference backstory is with what I call a Heavy Touch. This is where something from a player's backstory is taken and put right into the plot so the character runs into it. It can be done well or poorly like everything else. The point is that the backstory is mixed in with everything else in such a way that it comes up. The man Inigo is looking for that killed his father just happens to be the right hand man of the Evil Count that is the villain for the current adventure. Stuff like that.
Depending on the backstory though heavy touches can be hard. After all, if your whole adventure revolves around dragons trying to take over the world, how do you work in the Ranger's past of being a sheep herder from the old country? It doesn't really work in smooth
Fortunately, that is where soft touches come in. A soft touch isn't pulling elements from the character's backstory for the game so much as it is putting in places that reference the backstories. This could be as simple as describing someone falling into the pace of marching with an army fast and easy because they have a background as a soldier, or pointing out to that shepherd turned ranger that they recognize the mountain passes they're being pointed to as some kind of grazing trail.
I love soft touches because of how prolific they can be. You can bring things up all over the place, without having to change your plotting. Someone spent time as an entertainer? They recognize a tune. Someone has a family history of demon hunting? They've seen similar carnage in their family histories, which helps confirm that it is in fact demonic in nature. Someone has lived as a hermit forever? They are the ones who don't freak out during a long period of silence and isolation - it feels like home.
If you look for it, you can probably find a dozen places to reference your PC's backstories in your current game. And showing that attention encourages them to put the work in, and even bring it up themselves.
Give it a shot. It can do wonders.