When I bought this house and garden I inherited a fence of different ivies down the side passage along with Hydrangea petiolaris, all perfect shade climbers. I have kept them. They have have become very dense to the extent that both blackbirds and robins nest in the ivies and I have decided I love them. They are different leaf sizes, some plain, some variegated and I can see a mass of interesting greens, yellows and whites from my kitchen window as I write this - and it's there all year.
Many people don't realise that they also flower (small) and have berries which are really important for bees and birds at the end of the year. So, all in all, in the right place, they work really well and I would encourage you to keep ivies for the wildlife - if even in only a small part of the garden.
I now also have Clematis viticella running through them and Lonicera americana, so I have flowers on them too in summer.
To keep them in control, I cut them hard in December to use as Christmas decoration around the house. As decoration they look great, last a long time, are easy to twist around mirrors, lamps etc and, with a few holly berries twigs or tree lights interspersed, are truly great Christmas decoration.
I also have smaller leafed ones as trailing plants in pots, both at the front (which is North facing) and on the terrace. So they are great for evergreen, trailing pot interest too.
Some Hedera can take a little time to establish but, once going, they are reliable, colourful, evergreen cover for unsighly anythings - and great for the birds. Highly recommended.