Lonicera, or more commonly called honeysuckle, is considered by many to be a noxious weed but there are many varieties of honeysuckle that are not invasive but worthy additions to the garden. The bad guy here is Japanese Honeysuckle(Lonicera japonica) Now for the good guys:
Lonicera Baggesen's Gold - This is personal favorite of mine and I have grown it as a shrub, in a container and as a substitute for boxwood. It forms a mounding shrub with arching branches which are evergreen except in severe winters. The leaves are small and golden color.It lends itself to shearing, can be used as a tall groundcover, makes a great specimen plant and like all lonicera is deer resistant. it looks good with purple foliaged plants like purple smokebush or stands out next to deep green shrubs like rhododendrons.
Lonicera Major Wheeler is more like Grandma's honeysuckle. An 8 foot tall twining vine, it is a magnet for hummingbirds from late Spring through Summer. The trumpet shaped flowers are coral red. If you like yellow you might try Lonicera John Clayton. These vining Lonicera need full sun.
For shady, deer dominated areas Lonicera pileata is small ground covering shrub with beautiful glossy green leaves. This plant is one of The Pennsylvania Horticultrural Societies award winners.It can be grown in full sun or shade.An added bonus is amethyst fruits on mature plants. A somewhat lower version of this plant is Lonicera pileata moss green which has tiny paired leaves which provide year round interest. Both of these honeysuckles are evergreen.