If I understand your description with only a foot of space, there will be no direct light and not a lot of indirect light here, as well as probably little rain due to the buildings limiting what can fall here. With only a foot of space, even if you could get something to grow, any shrub will be rubbing against both buildings and will be a nightmare to maintain since you can't fit readily into such a narrow space to trim or remove plant debris, etc. I'd give up on this idea. Paint a mural on the wall or put some narrow artwork in the space or some interesting rocks.

My apologies, my description was incorrect, the space is between my driveway and my house, not the garage and my house. There is little direct light, but the area does get plenty of water and there is ample space to remove plant debris, pick weeds, trim, etc.

A picture would be great. It's hard to imagine the situation.

The picture is about a month old, but you can see the garage in the back and the strip of soil between the house and the snow covered driveway. It may be a bit wider than 12", but it's about 50' long. If there isn't any shrubbery that will grow there, I'd settle for a ground covering. As of right now, it just traps leaves in the fall, and weeds in the spring. I can install a dripper line if I need to to provide extra water as well. It connects to a flowerbed that sits under the front window.

if you are prepared for a certain amount of maintenance you could grow Coroneaster horizontalis against the wall or put in parallel wires and have an espalier of some description. Chaenomeles and Jasminum nudiflorum are often grown as wall shrubs under windows here. However, I don't know what your house is made of. Here most walls would be masonry so growing things against them isn't a problem. In the US you might be dealing with different materials.

Otherwise I really can't think of any shrub which would stay in that space without spilling onto the drive. A row of annuals or small perennials would be possible.

I like the idea of doing an espalier. The house is masonry so that should help. Is there any species of rose that would fair well in that space, or would the cotoneaster horizontalis be my best option?

I also like the look of the

Chaenomeles cathayensis

You now need input from people nearer your area. I can only say what works here.

I think a groundcover that can handle the Utah climate would be the best choice. Ask at good local nurseries.

If you ask on the rose forum about roses for that spot, adding the info (location, aspect, etc.) from here including the photo, you may get some suggestions that suit. There's also a Rocky Mountain gardening forum that's relatively busy (though I realize you aren't strictly in the Rockies) since the Utah forum seems to get very little traffic, so you can ask there about suitable plants in general. Look to see if there's any sun that reaches the wall, and how bright the shade is from the reflection off the house next door. Generally roses and quince/Chaenomeles like sun and a fair amount of moisture, but you might have bright enough indirect light at your altitude to make it possible. As laceyvail said, good local nurseries (if you aren't in too rural an area to have any) may have good suggestions for you.

Thanks for the help everyone