I used split Bamboo fencing, took it down in the winter months, just putting it back up again, its fixed to the boundary fence with bits of old wire.
Its various heights and lengths. Makes a nice natural background to plants.
Also try 'F' in the Goy encyclopaedia, lots of fencing ideas on there.

Trellis for plants to climb up and over too, it will soon be covered and give much more privacy. You could have a look at your deeds to see if there are any height restrictions in there.

You could try giant growing plants such as Miscanthus giganteus, Bamboo, some varieties of Arundo donax etc

Correction - I should have written its on sale at various heights and lengths. It would look a bit funny waving up and down along the top ! If you want a 6' screen, then buy all the rolls 6 feet high. I bought 5 rolls at £19 each
4 metres high (one per week to spread the cost) which covered about 60 feet, but that wouldnt be high enough for you.
The great advantage for me was that it didnt need fence posts. I wired it to the Council boundary diamond fencing & concrete posts.
Depends how long the neighbour's fence is.
Maybe they will get tired of leering over their fence, and think of something more interesting to do, like their garden.

Horrible things and not my perfect choice,but we planted Leylandii.Our Bungalow has 3 foot high wire fences on 2 sides,one set of neighbours on one side and three more lots opposite.We have a shared back alley and the main gate is just outside our fence,so EVERYONE spends all day walking past our garden and you just don't always want to chat,even though most of the neighbours are lovely....So hoping to grow a good thick hedge (will keep them trimmed of course or they're a nightmare!)
Have you got room for Leylandii Myshed?Trim them twice a year and keep to a managable height and they're fine x

No do bamboo - the really big stuff. the best thing is yes it may cost you a bit of money to get them, but the look on your neighbours' faces as it tunnels under the wall and up in the middle of their lawn will be priceless!

I know this as i had to take down a fence with exactly the same reasoning behind it, they were always staring at us when they were in the garden after they cut down a nice shrub that blocked line of sight.

So i swapped my rhododendrons for black bamboo!

all good suggestions, but my fave shrub for this job is portuguese laurel. They are evergreen, hardy, and grow a foot a year once established and fed.Have a read up about them?

more ideas here ... I hope this helps :o)

http://www.growsonyou.com/gardening/garden-screening-ideas