I do different things for different feeders. Crickets and grasshoppers I will release into the cage so they can hunt them down, because like Stephen said it provides exercise (not just to their bodies but to their tongues - tongues will get lazy if they don't have to aim for their food from varying distances) and is mentally stimulating. However, if I'm feeding roaches, I will put them in a little cup and have them catch them from the cup. And if I'm feeding worms then I'll either hold them on my palm, in tweezers, or place them on a branch near the chameleon.
The roaches will just hide in the first dark spot they find and then they'll give me a heart attach the net time I'm cleaning the cage, so I don't want them to be loose at all. And the worms may not move much or sit on a branch properly, so I like to hold those too. But things like crickets, grasshoppers, mantids, etc. will go free in the cage.
I prefer not to hand/cup feed 100% of the time. Some hunting is not just beneficial, but essential, in my opinion.