We like Bradford Pear trees for shade here.

Alder or poplar grow pretty fast.

www.fast-growing-trees.com/index1.htm

We planted Austrees.  I think the oldest ones are just 5 years old now.  They are easily 40 feet tall now.  No, you did not read that wrong.  40 feet.  I think it is too late to order any for this year.  You can Google their web site.  We are very happy with them.

Bradford Pears do grow fairly quikly but they are VERY bad about rotting and we had a 25 foot one break off 5 feet from the ground earlier this year. SS

Don't cottonwoods grow fast?

Quoted: We like Bradford Pear trees for shade here.

A pox on you!  Bradford's are probablt the worst tree you can plant, especially in NY.

Ever seen what ice does to the Bradford?

To the OP, you're probably looking at some type of pine.  I suggest white (for NY).  Plant 'em on 10 foot centers, staggered rows.  3-4 rows will make a hella screen a few years down the road.  You should be able to buy seedlings from your state forestry agency, probably cost on the order of $85 or so for 1,000 (!), more for containerized.

Here's what a nice old white pine looks like...

Screen from what? Air raids? Hah. Pine's shade is all up top. Something with low hanging branches would be better.

A guy down the road had a not so stiff wind break a bradford pear off AT THE TRUNK!

They are nice looking trees particularly when they bloom but a waste of time.  

I'd plant a few sugar maple's instead.

Faster growing trees are generally weaker.
Bradford pears self destruct at around 30 years from all the lousy crotches.
High angle crotches do not allow the separate trunks to join together very well, and eventually split.

Pin Oak grows fairly fast.  You'll likely see a large tree in your lifetime.  

Silver Maples grow VERY fast, but remember the faster the growth rate of the tree the shorter it's total life will be.  Drawback to Silver Maples is their "helicopters" or seed pods they drop in mid-spring.  

Ash trees grow great and are relatively strong.  Just have to worry about the emerald ash borer killing them.

+1 on the poplar

I'm in the North Country.  Surprisingly, regular old sugar maple can grow fairly decently if planted right.  I'm getting 18 to 24" of tip growth on trees planted 8 years ago.  I simply dug em outta the woods as 6 foot tall, thumb diameter whips.  They are 20 footers now.

I have several apple trees.  The cortland and chestnut crabs are growing VERY well.  The crab was a 36" whip 7 or 8 years ago.  Its a 16 footer now.

My best grower is a locust.  Not one of those damned thorny bastards.  A shade tree variety.  I'm getting an honest 2+ feet per yar tip growth.  It's not going up as much as out though.

Poplar will grow faster than anything.  I do not recomment it.  Its a junk tree, and has a bad habit of trying to take over everything.  Roots frequently begin to run the surface, and over time you have roots breaking throught the soil and tripping ya up.  Damned trees are soft, and damage prone too.

If you want good growth, dig a large hole.  When I plant a tree, the hole is huge.  The reason is simple:  The digging and filling process breaks the soils up, and permits rapid root development.  Then water like crazy.  Even potted trees have substantial root problems.  Too much top for too little root.  Most trees will do nothing for growth until the roots are established.  Once rooted well  the tree will take off.  The best example is an oak I have.  It was pretty busted up (deer problems) and a four year old four foot tall tree.  I trimmed it flat at the ground (levelled it).  It grew back the next year as a 3 foot whip, a roughly 6 footer the year after and its now a decent 8 foot +.  Its growing like that because its got a huge root system to support the top growth.

Big trees suffer root problems more.  As a general rule, expect NO growth due to transplant shock for one year per inch of trunk diameter.  You can plant a 4 foot maple whip and a $200 12 foot rootball landscape tree.  In 7 or 8 years they will be the same size.  I know:  I'm looking at two trees that were planted that way.

In addition to roots, plan on water.   My whips are planted in a shallow bowl-like depression to hold water.  They are mulched with straw to help hold moisture.  Each gets two 5 gallon buckets every day the first year.  Not going to be around the BOL?  Water the shit out of each tree when you are there.  Much the crap out of it.  Channel roof run off (via eaves troughing) to the general root area.  You can also set a five gallon bucket with a very small hole in the bottom as a trickle irrigator to help prevent drying the roots.  This water issue goes directly back to the root issue.  If the soil dries, it contracts, breaks teh hair like fine roots, and the tree gets inadequate water.  Its severely stressed, even if it lives.

Think roots and water and it'll grow like crazy.

Consider a few things about planting species and location:  

Deciduous or conifer.  I like deciduous near windows.  Shade for coolin gin summer, no leaves for solar heat in winter.  Conifers are a bitch for gumming shit up.

Consider root problems:  Wells, footer drains, septic systems

Think about soils and water.  As a aside I once planted several conifers when I was a cub scout some 30+ year ago.  I planted them the SAME DAY (same species). Once was planted at home (near the eaves downspout, and where it got fertilizer from the lawncare freak neighbor with ths Scott's perfect lawn), the others were planted in poorer soils, with no fertilizer, and NO supplemental watering.  

By the time I was 20 (some ten years later) the one at home (with water and fertilizer) was a decent 20-25 footer, with maybe an 8-10 inch diameter trunk.  The others were 8-10 feet tall, with 4 inch trunks.  Same species.  Same planting day.  Location, soils and water was teh difference.

if you have room plant several types, make a couple rows. Plant a fast growing variety for quick privacy, then far enough away plant slower growing quality trees. By the time the quick ones die off slower ones will be getting there

Poplar is already on the list.

The evil, thorny black locust grows fast, but also has a shorder lifespan.

Speckled Alder, Aspen.