Vines that will not damage brick or mortar
Here's what I found in Wikipedia, actually:
The plant secretes calcium carbonate, which serves as an adhesive pad and gives it the ability to attach itself to a wall without requiring any additional support. While it does not penetrate the building surface but merely attaches to it, nevertheless damage can occur from attempting to rip the plant from the wall. However, if the plant is killed first, such as by severing the vine from the root, the adhesive pads will eventually deteriorate to the point where the plant can be easily removed without causing any damage to the wall.
Here is something else I found that may be of interest to you about suitable perennail vines:
Native to the Himalayas, anemone clematis (Clematis montana) is widely used to accent fences, terraces and brick walls. The vine grows to 30 feet in length. Clematis prefers well-drained, nutrient-rich soil and a full-sun location. Well-suited to U.S. Department of Agriculture plant hardiness zones 6 through 9, anemone clematis is a twining vine that requires support. Common periwinkle, also known as vinca vine, brings greenery and bright blue flowers to the home landscape. Low-growing, disease-resistant, drought-tolerant and easy to grow, periwinkle displays deep green, shiny leaves. Vinca vines (Vinca minor L.) grow from 6 to 8 feet in length. The plant flowers in April and May. When used as a foundation planting under shrubs, vinca vine will not attach itself to brick, stone or concrete. Trailing periwinkle plants thrive in USDA plant hardiness zones 3 through 8. Native to California, California grape (Vitis californica "Russian River") is a striking vine that thrives in Mediterranean-type climates. Use the vine to hide unsightly fences structures or landscape features. The vine does not damage mortar in brick or stone walls or structures. If support is not provided, California grape provides an excellent ground cover. Other vines with twining stems include trumpet creeper, bittersweet and wisteria.