Joe pye weed or ornamental grasses come to mind first.

Of course, Joe Pye doesn't bloom all summer. But I do think the solution to this problem is a handsome ornamental grass--Miscanthus 'Morning Light' is, IMO, the most beautiful of all the Miscanthus and you also get it all winter long--also very beautiful--which you wouldn't with a perennial. The only time the area would be bare is after you cut it back in early spring. Then it's bare until regrowth, a couple of months.

Persicaria polymorpha would cover the fence, though it's about 6' high. Here, it blooms from the beginning of June into the beginning of August. After the flowers fade, they turn pink and remain attractive for another few weeks. After deadheading, the plant will still persist at about 4' tall. It will give a faster show and fill than an ornamental grass, but if you have room, a nice grass with a persicaria will look attractive the entire summer.

Goatsbeard is another big one, and does have a long bloom time for a perennial. It will take a couple of years, though, to get established. But there aren't any quick fixes in the perennial world, unless, in most cases, you end up with an aggressive plant on your hands. I think the grasses would be your best bet. Mix them up for interest. I esp. love the feather reed grasses.

I was going to say what anitamo said, use a mixture of plants for interest all summer long. Also, less risk of some pest taking interest in your entire "hedge," and much more valuable to area wildlife. You might want to include a few small shrubs. Is this area in sun or shade? Flowers that tall are usually good for cutting for arrangements. If you google something like "IL flowers for cutting" you should get tons of taller plants (and then later, vases full of flowers.)

what ninamarie said. defnitely.and miscanthus strictus next to it for contrast and foliage.
mindy
www.cottonarboretum.com/

Just a note: while I adore Persicaria polymorpha, it spreads at least 12 feet for me. An enormous perennial.

I would consider flowering shrubs to go in that area so that you still have something there on off season to disguise it, plus you don't have to wait each summer for the perennial to get the height you are wanting. There's some Hydrangea and Weigela that come to mind that would be in that general size range.
Cher

Ha,

I suggested Joe Pye weed, but the family gave it a big thumbs down because everyone thought it was ugly. Persicaria polymorpha looks promising. The other possibility was sneeze weed, which is somewhat tall and has nice yellow flowers with a long bloom time.

Paul

Just to clarify--are you looking for one plant for one spot (what I assumed from the phrasing) or are you looking for many plants to hide a length of fence? If the latter, of course you need a mixture of plants that would include shrubs.

Agastache Blue Fortune. Tall and blooms all summer. Mine is a few years old and about 3 feet tall this time of year but in a couple weeks will be at least 4 feet.
Clematis will bloom on top of the fence but you may want to plant something by the base so you don't see the fence.
If it's really sunny - perovskia - russian sage. Gets to be 4 feet and really pretty. Blooms all summer too and doesn't take too long to get big.
Roses - many get at least 4 feet and look great even when not in bloom.
Hydrangea if you have the room and it's part shade.
Of course, we're on the perennial forum so I'm not going to suggest other shrubs.