There are two good reasons for overwintering plants. Firstly, for some tender plants it is a necessity and I have in mind here, especially in more exposed gardens, Tree ferns, Canna lily, and some varieties of Agapanthus. The other reason is to nurture through the winter plants which would usually be treated as annual bedding and thrown away.
Commonly called Geraniums, Pelargonium will survive a winter under glass. In cold areas they are best in an unheated porch or conservatory, in milder areas they will be fine in the greenhouse. Geraniums need light, little water and cutting back will encourage the plant to bush out more in the spring as often over the summer Geraniums can become leggy. I keep about a dozen in the conservatory and 90% survive the winter. Once it warms up they can be planted back out into containers for a summer display. Fuchsia can be overwintered in the same way; cut back and brought into a frost free enviroment and kept on the dry side dormant until around March time.
The second image above is a variety of Nepeta which is commonly found trailing in hanging baskets and is very happy in the greenhouse over winter.
Why bother? As a gardener I would rather recycle plants. In common with many gardeners I am becoming aware of the many road miles undertaken to stock garden centres now that small nurseries are so rare. We cannot turn the clock back to times past when garden centres grew a lot of their own plants, but we can recycle more of our own.
And another fear which has recently been flagged up is that many of the plants we buy from garden centres, even those sold as bee friendly, are, perversely, covered in pesticides. If this concerns or interests you the Independent's article is a good starting point with the recommendation gardeners try and grow more of their own to avoid contaminated plants from garden centres. It rather looks as if winter may come early this year be ready to bring plants under cover.
More advice on how to overwinter plants