In a small garden the last thing you need is to feel hemmed in by very visible walls. In a small garden, like mine, all that extra vertical space a wall provides is usually appreciated as extra growing space, whether for the evergreen of a Garrya elliptica, the berries of pyracantha, or the many-hued clematis varieties.
I know from experience that the temptation is to rush into planting anything
green that will grow against them and cover them up . . . even if the plant
chosen may end up covering up not only the wall but virtually the whole
garden . . .
In my previous yard garden I planted a Russian vine (also known as the Mile-a-Minute vine) to provide quick cover. Like many other people before me and since, I regretted it later (see truly tiny gardens). Here in this garden I've got more space but have still found that certain climbers, once established, are hard to control and keep within an allotted space. If space is restricted, or your walls are low, I would think carefully before planting a jasmine or a Parthenocissus quinquefolia. Others I've struggled to keep to a reasonable size are Solanum crispum 'Glasnevin' and Akebia quinata. The Humulus lupulus 'Aureus' is also vigorous and can cover a large area, but being herbaceous it dies back and starts its spring growth each year from its base, so is easier to control.
The fast and vigorous growers are fine as long as you don't mind a high-maintenance garden that needs regular pruning.
I do think it's important to get the boundaries of a small garden covered
as quickly as possible with greenery, as this makes a garden more effectively
blend in with its surroundings - whatever they are - and even an ordinary
plain green ivy looks better than line upon line of orangey-red bricks.
Older brick is more subtle in colour, and also less regimented in appearance.
Covering it all may not be necessary. Still though, I've found it more pleasant
in winter to look out of the window into the garden now the end wall of
my garden is beginning to be covered with the evergreens
I planted against it. In previous years, with the abundance of summer gone,
I've noticed how in winter the walls of my garden seem to close in - in
that they're suddenly very visible from the house.
I've planted in front of the wall I view clearly in winter a few evergreens, Fatshedera x lizei, Choisya ternata, and Solanum jasminoides 'Album'. There's also a white spring-flowering clematis, which isn't interesting in winter, but will be something new to look at in spring.
Planting against walls is often dictated by the aspect - whether it's
a sunny wall facing south, a shady one facing north, etc. I spent a long
time in the early days of gardening poring over lists of plants for each
aspect, and occasionally worried when I saw that something I'd planted facing
north was in someone's list as suitable for facing east. It took me a long
time to realise that though there are certain basics that everyone seems
to recognise from their experience to be true, for instance that lavender
bushes hate sitting in wet soil, and just die off, other accepted notions
are open to question and to your own experimentation.
After all, most houses and gardens don't tend to be laid out on some kind of rigid grid, with one wall facing south, one facing absolute north, etc. Most of them are more north-west, south-east, that kind of thing. Also relevant, particularly in towns, is the presence of other buildings, which may create shade by blocking out the light whichever way your wall faces.
The following are plants that have thrived when grown against the walls in this garden. The links are to photographs, where available, and the position is given.