Some of my favourite plants both in the garden and the wild, are climbers, with clematis and wisteria counting in my top ten for any garden. There is always something to suit everyone and any taste.
There are delicate pretties, refined lady’s and brooding mysterious blooms.
You will be able to find a plant for any situation and they will thrive and strive to reach the sky.
Below are some of my recommendations:

Bright, sunny and open positions
Clematis Montana is a fast growing climber that can reach up to 40ft. Not for a small garden.

Seaside and windy locations

Campsis Radicans vigorous and woody it should stand up to most weather but a bit of shelter would give it a hand. Lovely orange tubular flowers.

shady and woodland areas

The reliable Lonicera (Honeysuckle) both beautiful and sweetly scented.

Urban contemporary settings

With contemporary gardens its best to keep it simple but that doesn’t mean boring. Virginia creeper has lovely large green leaves which turn bright red in autumn. Its capable of climbing most things with suckers so no need for fussy obelisks.