I think the fix would depend on what is causing the problem. As manufacturing technology advances, the tooling and molds are able to make panels more precise so the gaps are smaller than in older cars. But, plastic is still plastic and it will deform over time with exposure to sunlight, temperature swings and other environmental factors. So, it will loosen up where it's mounted and relax/settle where it's not so supported.
If the problem is a loose mounting point, such as where the plastic tab of a trim panel snaps into a metal hole in the body, I'd tighten up that connection rather than try to brace the entire panel elsewhere. I was installing an iPad mount into a new (at the time) 2010 Sierra Denali and noticed each of the holes in the dash where the bezel snapped in had felt tape surrounding it. Having ripped apart the dash on my S10 and other similar-era vehicles, that was something new to me. A simple but effective solution that the factory took the initiative to install. You could do the same with your trim panels to tighten the hold and insulate the parts from each other. Just get some felt tape with adhesive on the back side, cover the hole and cut a slit in the middle of it with a razor (an Xacto knife would be ideal) for the trim panel's tab to go through.
Using felt buffers such as what Wes linked to would be great for the areas where a panel rubs and makes noise. Some points need to flex independently of the parts they're attached to, so trying to "glue" them down to those parts won't work. Instead of trying to secure them, just insulate the contact point with felt so the panel can rest on in and move as needed without making any noise.
Way back in the day, with my Civic and S10 (both had decent sound systems with big subwoofers), I played bass notes from an Autosound2000 CD to make the interior panels rattle and buzz. Different bass frequencies resonated with different panels and made them vibrate. I started with the lower frequencies and addressed the rattles and buzzes as the occurred. Of course, the mid- and upper-bass coming from the door speakers revealed all kinds of buzzes from the door panels. This made sense since it was a giant piece of plastic snapped onto a metal door that was slammed thousands of times throughout it's lifetime. Replacing the "Christmas tree" pins with fresh plastic ones and insulating the holes in the door which they snapped into alone made a huge improvement. I also superglued small blocks of foam rubber behind the lock and latch rods to keep them from vibrating against the metal door frame and applied felt tape along the door frame frame where the edge of the panel contacted it.