Woody stems are one of the things that take a very long time to decompose. They are definately somthing you should avoid putting into your compost heap simply because of the length of time they will remain there. So what can you do with them? Here are a few ideas;

• Bundle smaller ones together and hang them in a sheltered place to make a home for lacewings
• Shred the smaller ones and use them for mulching, Ours go in the chicken run, it helps reduce the smell and encourages bugs for the chickens to scratch around for. 
• Make a pile under a hedge, you might strike lucky and attract a hedgehog but you'll also provide a habitat for all the creatures that like to make their home in dead wood.
• Make an attractive feature in a border out of some of the more interesting ones - sculptural branches can add structure and height to a garden and make a good place for climbing plants to cling to
• Buy and fit mushroom spore plugs to some and cultivate your own supply of edible fungi
• If you have a log burner or open fire you can burn them and use the ash as a soil conditioner or add it to your compost heap.

This is just a small selection of idea's. If you have seen or tried something else let me know and I will add it.