Campsis radicans
The trumpet vine or Trumpet Creeper (Campsis radicans), also known as Cow Itch Vine and (in horticulture) as Hummingbird Vine, is a large and vigorous woody vine of the family Bignoniaceae, covered in flowers during the summer and a magnet for hummingbirds. It can become overly aggressive and reqiuires annual pruning in some situations. Good along fences or a great ground cover for that eroding slope.
If you want something more delicate and manageable, consider the Lonicera sempervirens (trumpet honeysuckle) or Bignonia capreolata (cross vine).