I've grilled asparagus, with a little bit of olive oil brushed on. I've done it loose on the grill and I've also taken smaller wood skewers and put them through the butts and tops of the spears so I was able to flip the whole package at the same time.
I've grilled pepper quarters, too, with a little brush of olive oil on the skin side. I have discovered, though, that you can't prep meals ahead with them - they give off a lot of liquid when reheated from the fridge or freezer.
When I do kebabs with chunks of peppers, red onion, zucchini, whatever else you want to put on there, I do a separate skewer of small tomatoes. I find the tomatoes cook faster than everything else and are about to fall off if you put them on with the other veggies.
You can take the husks off the corn and grill it direct, too. It'll get some blackened bits, though. Or you can take the unhusked corn, soak it in water and then grill it. It'll steam in the husks.
My vegetarian friends have used one of those perforated baskets specifically for grilling veggies and tossed them around in there like they were doing a stir fry. Those were good, too.
I bought a new grill a while ago, with three separate burners. I've kept the grill over the right most burner clear of meat so when I have my vegetarian friends over, they can have a 'clean' section of grill.
My favourite way to do potatoes on the grill? Either slice them or chunk them, with the skin still on. Spray the foil with Pam or use a little olive oil. Put the potatoes on then add fresh garlic, wild leeks (you could use onion, instead), a couple of fresh sprigs of rosemary, seasoned salt and pepper, then drizzle with olive oil. Wrap up the foil and bake on the barbecue until done. Remove the rosemary sprig when serving so no one gets the 'tree'. The leaves left behind are fine.