Black-Eyed Susan Vine  (Thunbergia alata) is, although a beautiful flower, also highly invasive. If you grow it at all, keep it in a pot.

Cardinal Creeper  (Ipomoea quamoclit), also known as cyprus vine, is an annual in temperate areas. Large red flowers will attract hummingbirds.

Cathedral Bells  (Cobea spp.) are vigorous climbers with large flowers in purple, white or other colors.

Hyacinth Bean Vines  (Dolichos lablab) produce lilac flowers and bright purple pods. The pods and beans are toxic, however;  just grow these for show! Hyacinth Bean Vine seeds 

Moonflower  (Ipomoea alba), a close relative of the morning glory, has large white flowers that open at night and release a sweet perfume. Grown as an annual in temperate areas.

Morning Glory (Ipomoea tricolor), the always-popular climbing vine, comes in a wide variety of colors and is usually planted as an annual in temperate areas. 

Honeysuckle  is loved for its sweet fragrance, but L. japonica (Japanese honeysuckle) is an invasive weed in some parts of the US; try to find native species instead, such as trumpet honeysuckle (L. sempervirens).