This month lots of plants are going to seed. Many things will self-seed, and so you can leave them to scatter their own seeds and enjoy the new plants next year (many wild flowers are particularly good at this). However, gathering the seeds means that you can plant them more selectively (losing less to rotting and birds, and also choosing where to put them), or you can even give them away (a home-made packet of seeds, perhaps with other produce from the garden or gardening tools can make a lovely Christmas present).
My sunflowers have finished blooming, but the heads are heavy with the seeds. I snipped off the flower heads and hung them inside to dry. During the winter I'll hang them outside on trees to make home-made bird feeders. I did this last year, too, and our garden was full of little birds all winter long.
My broccoli plants also went to seed this year. I've never tried gathering broccoli seeds before, but I gathered all the seed pods and hung them to dry inside as well. When they're all dried, I'll collect the seeds in an envelope and store them for the spring. Make sure that the seeds are completely dry so that you don't have problems with mould. We'll find out next summer how the home-harvested seeds have done, but I'm excited to try it.