North east facing wall

Clematis comes to mind - several will tolerate quite a bit of shade and they all love their roots in the shade.

Wish the edit function was fixed! I wanted to add this list:

http://the-plant-directory.co.uk/climbing-plants/clematis/clematis-for-full-shade

Have a look at the climbing hydrangea - hydrangea petiolaris - I think it would be emminently suitable for that position. http://www.crocus.co.uk/plants/_/climbers/other-climbers/classid.1665/

Clematis came immediately into my mind.

Consider the rose Madame Alfred Carriere.  It is a stunner on a north wall - beautiful noisette blossoms with blush pink buds opening to creamy white.  Smells beautiful. Repeat flowere.  Healthy.  What's not to like?!!

Climbing rose -  Zephirine Drouhin lovely perfume, thornless and happy even on a north wall see link for picture.  I have it and Madame Alfred Carriere and both are lovely. Also have hydrangea petiolaris but it has been slow to take off. They are all growing on my north or north west facing and I have 2 clematis on my Northeast facing walls. One is Clematis Comtesse de Bouchard but I can't remember what the other one is<span style="font-family: verdana,arial,helvetica,sans-serif; font-size: xx-small;"><span style="font-size: 13px;"><span style="font-family: Times New Roman;"><span style="font-family: verdana,arial,helvetica,sans-serif; font-size: xx-small;">.<span style="font-family: Times New Roman; font-size: small;"><span style="font-family: verdana,arial,helvetica,sans-serif; font-size: xx-small;">

http://www.classicroses.co.uk/products/roses/zephirine-drouhin/

Also thought of the climbng hydrangea, always looks stunning on a cool wall.  

It's not just the way it looks in the summer - in the winter you get the benefit of a beautiful tracery of reddish stems on the wall, and we find it's a favourite place for blackbirds to build their nests in the spring 

I'd go for the hydrangea if you want a fairly densely-covered green wall - its a lovely fresh green and the white flowers are long-lasting and beautiful. Thats the way to go if you want simple, clean and fresh. Its a low-maintenance option too as it'll self-cling after a bit of initial encourgagement with a few temporary wires and only needs to be pruned if you want to.

If you want more flower than foliage and don't mind giving it all a bit more attention in terms of pruning and tying-in, I'd have one of the above-named roses plus a clematis (or even two!) through it. Most clems and all roses want some sunshine on their heads, but by no means would want it all day long - their petals are delicate and will frazzle in baking heat. Both would prefer cool, moist, rich conditions at their feet. The hydrangea likes the same, but would tolerate drier, poorer conditions.

Honeysuckle may also be worth a look if you're a particular fan and don't mind keeping it under control.

Spoilt for choice! x