Make one side of image fade to transparent with GIMP?

Updated for GIMP 2.10: You can put all your layers into a layer group, then add a layer mask to the group, and paint a white-to-black gradient on the mask. Initialize the layer mask to "Black (full transparency)", so that the black part will be transparent. The benefit of using a layer group is it's non-destructive so you can continue to work with your separate layers.

If you only have one layer to start with then you can skip the layer group and just apply the mask directly.

If you wanted all sides to fade to transparency, you could start off with a black layer mask, then draw a white rectangle inside it, and apply a blur. In any case, I think starting off with a layer mask is what you want.

In earlier versions of GIMP you can still do this but you need to flatten your layers into a single layer first then apply the mask to that layer.