The trellis I made from branches trimmed from an overgrown elderberry took "rustic" to almost laughable levels, but my pea vines grew up its supports just the same. The trellis was completely free to build and even survived the winter. My peas haven't sprouted yet this spring, but when they do, I will train them up the trellis I made myself.
For most of these projects, new growth pruned from shrubs or trees work best. In my garden, elderberry, lilac, and cherry trees produce the long, straight branches that I need. Willows are a great source for pliable whips (very small, flexible pieces of wood pruned from new growth), but green wood from many other shrubs and trees can work as well. Here are five things anyone can make with garden debris.

Trellis

To make the trellis for my peas, I buried two pairs of elderberry staves in an inverted V on opposite sides of a raised bed, tying them together with twine at the top. Then I tied a piece of wood on top like a ridge beam. I dug stakes into the ground where I wanted my vines, and ran twine over the beam. Voila! So easy, even I could do it. There are lots of other equally simple structures you could make. You could grow your vines around a teepee made of dried cornstalks or pruned branches. Another approach is nail two branches into a T shape and use stakes and twine to create a lean-to. For a more solid look, replace the twine with additional pruned branches.

Cloche

When you're trying to save tender plants from frost, you don't need to be fancy. First make a simple teepee by tying four pieces of pruned wood together at one end (the size needed would be determined by the size of the area or plant to be covered). Stick the other end of the sticks into the ground around the area to be kept warm, and wrap the structure in clear plastic. You can use the heavy plastic sold at hardware stores, or save drycleaning bags for the purpose. Floating row cover fabric is another good choice. For vegetable gardens that have just sprouted, you can bend whips into hoops that will lift row covers off of seedlings.

Plant Markers

Cut and sharpen stakes from pieces of pruned wood (about the thickness where hand pruners stop working). Using a vegetable peeler or pocket knife, scrape the bark off of one side of the blunt end. Carve, paint, or write your label with marker on the exposed inner wood. Push the sharpened end into the ground near the plant you want to identify. For an even easier project, you can paint labels onto pieces of broken terra cotta pots. Are all your pots in good condition? Save the rocks you find when you're digging in the garden and paint those.

Edging

If you find a lot of big rocks when you're digging in the garden, you can use them to edge your beds. If you have a lot of blow-down after a winter storm, or must remove a tree entirely, consider edging beds with small logs stuck on end (dig a trench as if for brick edging to help them remain standing); cover twice as much area by chopping the wood lengthwise and using half-logs. Or you can make the most of waste wood by slicing off "cookies" and using the disks as edging.
On a recent trip to Oregon, I saw a traditional willow-wood corral and realized that it would be easy to make a raised bed using the same technique. Instead of nailing 2x4s together to make the raised bed frame, simply insert pairs of stakes around the perimeter of the bed and layer small branches between them.
If you want something that's more ornamental than structural, you can bend whips into rainbow shapes to create a scalloped edge around your planting beds.

Furniture

Instead of grinding out the stump of an old tree, carve it into an armchair. If that's too hard, smooth off the top for a perfect teddy bear's picnic table. Large logs can be leveled and turned on end to make stools for rustic garden seating. If you have the tools and your skills are a little more advanced--okay, a lot more advanced.
The trick is to look at what you have and get creative. When you let your imagination go, the possibilities are unlimited, regardless of your skill level. If you really get stuck, you can always search Pinterest for inspiration - just don't let what you see there intimidate you.