Yep. I just recently lost my therapy doe (she would go round nursing homes, hospitals, schools etc) and she knew the following voice commands:
walk on
steady (slow down)
whoa (stop)
gee and haw (left and right)
stay
wait (variation on stay, she needs to stay there but can shift around, sit down, stand up etc. as opposed to stay when she isnt allowed to move a muscle)
leave (as in leave it, if she wants to grab something in her mouth)
hop in/hop up (to get into a car or on the truck)
stand (stand still and 'brace' so that someone can lean weight on her or use her to pull themselves up)
My harness and pack guys are trained to be driven by voice commands, walk on, steady, whoa, gee and haw, they also know stand and hop in. Two of them (Charlie and Chaplin) will drink out of a coke can on command. One (Charlie Jnr) will open a gate on command (thank god he's not smart enough to do it all the time). Another of my wethers (Gizmo) will rise up on his hind legs on command. I also have a doe (Spot) who is trained to climb up a ladder and down the other side, she will also turn in a circle on command. We are practicing it at ground level now, but soon I will put the two together and have her climb the ladder, stand on the platform at the top, and turn in a circle. And I have one more doe (Calamity) who will jump onto a 44 gall drum and balance on it while it rolls around, she is slowly learning to move the drum along a set path.
So yes, goats can be trained, they are very intelligent and that is both a good thing and a bad thing! I find they respond better to clicker training than treat training - goat brains fly out the window when food is involved.
I have a show doe who will open her pen at the show, then walk down the aisle and open the pens that her two friends are in. Seriously, I was gobsmacked when I first saw her do it. I definitely didnt teach her that!