You don't want anything that will adhere to the wall. That would be ruinous. I suggest that you construct an attractive lattice so that you can grow something which will climb that way, rather than with permanent little suction cups! YIKES.

You may get some good ideas in the Houseplant Forum, for vines that will grow well inside. What is the sunlight situation?

I agree that it would be disasterous to have anything clinging to dry wall (plasterboard) directly. If your walls were all stone, concrete, cinderblock, or brick, that would be different.

Some of the most popular "indoor" vines are pothos (which can cling to those bark-covered wood stakes and philodendron (eg., split leaf philos) that can similarly be trained against that type of support and can cling with aerial roots. These are common tropical understory plants that are adaptable to the low light and lower humidity of a typical indoors environment. The problem with plants like ivies indoors for climbing purposes is that they need alot of humidity around them and on any surface that they might be clinging to, which is do-able if they are in a hanging pot but more difficult if they are climbing up high in a house. and may need to be tied to the support. A pothos seems to be a bit more able to handle dry air than ivy (perhaps because it perhaps evolved in areas with distinct rainy/dry seasons).

Other possible common indoors hangers/climbers would be hoyas. There are dozens of species and if given a support, they will go travelling (they are twiners)!