Usually, the websites offering desktop wallpapers whether for free or not, have their whole database of wallpapers divided into categories, in order to ease the users' searches. And most of these websites have a special category, a more dynamic one, a category of top wallpapers, where you will find the wallpapers other people have liked and used. If you don't have a certain preference for as far as what the wallpaper should have as main theme is concerned, this kind of category should be very useful. Usually top wallpapers are mixed ones, so there you might find pictures of landscapes or animals, but also of bands or movie stars.
But if you are not particularly looking for the top wallpapers, regardless of what they represent, and, for example would like to have a desktop wallpaper with your favourite band, on categories like Entertainment or Music, you will most probably find what you need. Even more, some of the websites providing this type of services have top wallpapers subcategories in every major category. So all your problems seem to have met their solution. If you want a wallpaper with one of your favourite movie stars, a good way to start searching is by looking first at the top wallpapers in movie stars categories and sees which ones are the most requested for the week. But you can also search for top wallpapers in categories related to nature, to wildlife, amongst pictures of flowers, gardens, landscapes, animals, birds, movies, TV shows, animation or any other possible category. If some major holiday is approaching, most of us like to change the desktop background and make it more appropriate and related to the event. So you can always go searching for top wallpapers related to Christmas, Easter, Valentine's Day, Mother's Day, Halloween, or any other holidays, events or special occasions.