Not to everyone’s taste but Ivy or Hedera species are the most frequently grown, year round, climbing plants. Try these alternatives.

5 Top Evergreen Climbers

Solanum crispum ‘ Glasnevin’ is a shrubby climber that needs to be tied in to wire supports. It will repay with prolific blue blossom with yellow stamen during summer and autumn.
Lonicera henryi has purple flowers followed by small black fruit. It is a good twining and climbing plants to grow up vertical supports.
Lonicera japonica variety Halliana is another honeysuckle this time with scented yellow flowers. It will only loose the leaves if the winter is exceptionally harsh and cold.
Trachelospermum Jasminoides is heavily scented when in flower. It grows aerial roots and like most scented climbers prefers a warm south facing wall.
Clematis armandii flowers in late winter and covers a large area such as a wall or fence clinging with twisting leaf stalks.

Evergreen Ivy Tips

Try a variety other than common Ivy such as Hedera colchica ‘penata variegata’. You get better colour or leaf form but retain all the benefits.
Ivy provides food and shelter for wildlife and a year round backdrop for your garden.
The aerial roots should not damage a sound wall but the young rootlets may loosen bad mortar.
The leaves can be plaited to create wreaths or used as a filler in decorations.
Ivy can be grown on steep sloped as ground cover that protects soil from erosion.

Photo credit
Kew 056e by Michelle Bartsch CC BY-NC-ND 2.0
Ivy by R~P~M ‘Ivy leaves at sunset, Lower Salden Farm, Mursley’ CC BY-NC-ND 2.0