How can I make home-made veggie burgers stay together so I can grill them?

I second the recommendation for Lukas Volger's Veggie Burgers Every Which Way. I've been working my way through it and have made several of the recipes so far, all of which have been good. However, I would say that not all of the recipes in the book work well for the grill.

I've been doing everything vegan from the Volger book with mixed results. Many of the recipes use eggs, but you can do them with just breadcrumbs and water as the binder. They come out pretty delicate that way and are better in a skillet and then baked, as Volger recommends. His tofu and chard burgers use some tofu that has been browned then pureed as binder. This works ok, but the burgers came out quite delicate (but still delicious).

Silken tofu pureed in the food processor gets a thick, creamy texture that could also be used as a binder.

Eggs are by far the most common binder as they may be the best edible binder there is, since they are basically liquid protein, but obviously not vegan.

For delicate burgers, I use this cooking grid on the grill, which works great. You can find something similar at most kitchen stores.

Another binder option is steamed rice, prepared like you would for sushi. It gets sticky and makes a great binder, though they'll still be a bit delicate. I've been making the beet, brown rice and black bean burger recipe from Volger's book. I add bbq sauce and a paste of pureed rehydrated prunes, similar to the veggie burger at Hillstone/Houston's restaurant and they come out really great. They work fine right on the grill, though refrigerating them overnight makes them a little sturdier.

Another option is adding vital wheat gluten and water, aka raw seitan dough. This is what is done in the Veganomicon black bean burger recipe. I tried these straight on the grill also and they stayed together perfectly, as well as any commercial veggie burger. However, they were a little bland and could use some more seasoning.

I haven't tried any of these in burgers, but some common binders in vegan baking are peanut butter, apple sauce and Ener-g egg replacer. I bet peanut butter would work well in a burger with flavors that work with peanut, like Thai flavors or chipotle.

Falafel-style burgers also don't need any binders, they stick together pretty well and can be grilled, though you may want to use a grill grid or something similar.

Lastly, you can put a cast iron skillet or pizza stone on the grill - it's common now for grilled pizza and will work for delicate burgers.

There's a lot less fat in most veggie patties compared to most meat patties, so add extra oil to the grill (using an oiled cloth). You can also freeze vegetable protein based patties first (they stay together longer), and let them cook for long enough before trying to move them.

It may just be your recipe too, it may be too wet (or too dry). Try a recipe book like Veggie Burgers Every Which Way for inspiration, which has a huge selection of tasty veggy treats.

How were the burgers shaped? If formed firmly in a press rather than just scooped out and hand patted, air pockets would be reduced and a nicer edge created.

In a skillet, I pack heavy wet burger mix directly into rings and let the bottom crust form before lifting out ring. No breaking apart upon flipping. For grill...trickier: maybe cheat badly and first give a quick zap in the microwave just to set. Alternatively, freeze and pop onto grill.

I'm sure I already mentioned that in a related question, but this is needed for completeness here:

Chickpea or lentil flours work well for binding - they bind like billy-o and are also very rich in protein (nutrition OT or not, using something nutritionally similar as a substitute is always a bonus) - make sure they patty is cooked long enough for these to properly set, they taste bitter when raw and yolk-y when undercooked...

If the patties are still too soft, grilling/pan frying them then finishing them in the oven can improve them a lot.

Make sure all patties have gotten to room temperature on the surface, apply oil to surface of patties and grill's grate, have at 'em. This technique worked for my vegan naked fatties, and I'm sure it will work for burgers. That said too much bread/starch will cause sticking. Add corn or (black) beans to tinker with that if the oil trick doesn't work.

Some creative answers were given. I have had some good success with adding some cooked oatmeal to mine (I don't use instant oats, but that might mask the presence of the oats).

If they are still crumbly, you may also want to line your grill with aluminum foil to create the effect of a skillet and allow them to hold in place while cooking.

Flax eggs are the answer you are looking for.

Use corn starch to mix them. Corn starch stick the ingredients.

If you use the "fake ground beef" then they will always fall apart!! Try using tofu instead! Just buzz it up with your other ingredients (like sweet potato!) and they will make perfect burgers which stay together! The ground beef will never stay together!

You can use arrow root as a binder