ski areas with the most extensive and exciting green trails?

You should probably start close to home. Bretton Woods.

Not that they are necessarily, the best green runs, but both are very long and allow a beginner to really feel like they're going somewhere. Burnt Stew accessed from cat track off peak Chair at Whistler/Blackcomb.. The chair itself is epic and the views unbeatable. Home Run from the top of Bonanza chair at park City Mt. Resort. Big and wide with some variable terrain from top to bottom. Fun cruising even if you're not a beginner.  

Polecat trail at Wildcat is one of the best greens in the Eastern US.  Great Eastern at Killington (on a quiet day), Dreamweaver and Upper Mtn Rd at Okemo, La Familiale at Mont Sainte Anne, Schoolmarm at Keystone (Keystone's Dercum Mtn has a whole bunch of greens and blues), Corona Way at Winter Park, Loveland's got a bunch of easy green above tree-line terrain, Perimeter Trail at Heavenly, some very wide greens at Powder Mtn, UT, some beautiful greens at Alta.  Lots more...

You know that the rating system is only relative to each particular mountain, right? Whistler Mountain does have a lot of green trails, but many of these are steeper or more difficult than greens at other mountains. I still enjoy skiing most of Whistler's greens. It IS very cool that you can ski green trails from the very top of Whistler to the bottom, but the top isn't really the laid back cruising you're after--the Burnt Stew trail is fairly narrow and has a lot of flat or even uphill spots. This isn't to put you off, just don't expect wide gentle cruisers when you see those green dots on Whistler.

Sun Valley also has a lot of greens, and they are so beautifully groomed and the fall lines are perfect. But their greens are as steep as some resorts' blacks. I think they are a lot easier than Whistler because they're so wide, nicely groomed and uncrowded. So again, it just depends on what you find hard. Here's a picture of a typical green off the Seattle Ridge chair. It's super fun cruising and not just for beginners.

You can't top Mt. Bachelor for long greens, decent snow and great grooming especially late in the season.

And thus completely useless in answering questions like the OP's.  Whistler/Blackcomb is one of the worst places for beginners IMHO.  Truly gentle terrain is confined to the base areas with unreliable snow surfaces.  Most of the greens at Whistler and the main mountain Baldy at Sun Valley are too steep for most beginners, pictured Seattle Ridge being a perfect example. There are some places where many of the blues are quite suitable so much more terrain is available. Keystone, Northstar, Park City and Snowmass come to mind. June Mountain (1/2 hour north of Mammoth) is excellent. 

I still don't get the flat reputation at Bachelor.  In the universe of western mountains it's fairly average in pitch.  That means the greens are comfortable for beginners but most  of the blues are not.

If the trail map has length to vertical ratios for its lifts, beginners should look for lots of chairs with ratios of 5 to 1 or more.  This is the best way to use a trail map to assess terrain.  Ignore the color trail ratings which are relative and usually don't stray too far from the 25/50/25 marketing ideal.

Quote:

Originally Posted by Tony Crocker 

...Park City and Snowmass come to mind.
 

+1 to these two.

I think Beaver Creek, Telluride, and Snowmass give you the best chances of having a great green-level cruising experience in a beautiful big-mountain setting.

Beaver Creek has some great green runs at the very top of the mountain. You can stay up there all day or stretch it out and continue on to the bottom on one of the greens like Cinch or Dally.  When you look at the trail map, it doesn't seem like there's a lot of beginner terrain, but when you get off the lift at the top of the mountain, it feels pretty expansive.

Telluride also has a fair number of relatively long, wide, low-angle runs that are probably a little too steep for never evers but would be suitable for an advanced beginner; they are rated with a double-green circle on the trail map.

It's been a long while since I've skied in Summit County, but I seem to remember some nice options at Breck and Copper also.  Keystone always seemed a little too icy and crowded whenever I visited there.

Steamboat comes to mind here--the blues in the Sunshine area are wide and gentle and more like greens at many other resorts.

In terms of sheer volume of beginner friendly terrain, all 3 of the big Summit County resorts are hard to beat.  But they are busy and a lot of beginners are not comfortable with heavy traffic of much faster skiers.  As I witnessed first hand at last year's Gathering April is when Summit County is at its best with maximum coverage, usually good surfaces with the high altitude and the crowds more manageable. 

For quality and aesthetics of the beginner terrain I agree with Gnarlito that Beaver Creek, Telluride and Snowmass are good choices.

Peak 9 at Breckenridge is a novice/low intermediate paradise.  Lots of skiers and riders, but lots of trails to spread them out on.

Snowmass is really nice, but don't forget about Buttermilk.  Basically the whole mountain is beginner friendly, except for a few easy blacks.

Bretton Woods has already been mentioned, but specifically the great thing about their green trails is that they have 4 top to bottom runs that are all green. Don't find that many places.

Bretton's Wood/Big or Bigger Ben trails tends to be a bit crowded being right in front of the lodge and under the Bethlehem Express, but is usually a nice trail to start the day out with.

Right next to that run to the skiers right is Sawyer's Swoop which usually somehow manages to avoid picking up a crowd despite being right next to the perpetually crowded already mentioned run. Although there seems to be some issues with the trail absorbing water run off and getting icy or even wet in one or two low spots, but they are usually well marked and roped off. 

Farther from the base lodge off the Zephyr chair is Range View. It is a fun cruiser regardless of ability level. Range View is also a nice beginner trail in that they only groom the center of the trail, so the sides have some nice small bumps that are good for learning on. 

Perhaps my favorite trail at BW is the green cruiser on the West Mountain known as Avalon. It has spectacular views and is a great trail to just cruise on. It can get crowded at times because it is a feeder to the West Mountain area, but usually is in pretty good shape. 

I think generally, any run that is REALLY LONG is probably a great cruiser for a lower level intermediate.  That being said, I didn't chime in with this resort because our longest run as some less than easy sections, depending on conditions, plus we've got fog and lower level skiers are frequently intimidated by fog. The long cruisers here frequently have people straightlining them that couldn't buy a turn if they wanted to, which to me is not the best place for a zigzagger to be.  

It would help if you clarified the "skier level" involved.  One resort's green may be another resort's blue (not sure it would ever be black anywhere, but you never know...)

Once again, define beginner.  Are you looking for THIS, THIS, or THIS (last one has green sections, but is mostly a blue).

IMO, there are beginner runs and then there are green runs.  For the low level skier, the difference between what I would call a "snowflake" trail and a green trail can be heart-stopping.  I well remember a never-ever panicking on a slope that was close to a parking lot years ago when we had guests come to see us.  It's all relative.  

If all you want is WIDE, then many intermediate runs during non-holiday period weekdays would fill the bill.  Add in weekend traffic, though, and it could be suicidal to be zig-zagging back and forth across the whole slope.

If you don't know the level skier you are, refer here.

Deer Valley

Telluride

im pretty much a beginner and have been to these two places. Deer Valley was the first place i ever put on a pair of skis. Ive been twice. PCMR is right next door as well. But i preferred DV.

Telluride, if i remember has some really long greens and the scenery is incredible which was already mentioned. 

People say Tride is hard to get to, but i didnt think it was bad. Lots of flights right into Montrose and then a $50 or so shuttle. No car needed. 

i like to get trailmaps on line, look for trail names, then look for them on Youtube. Lots of vids of lots of runs out there. 

http://youtu.be/jQ75HAorERY

A Europe plug here - Ski Amade in Austria (825kms of pistes) will serve you well. We came back from a school ski trip just a week ago and it was amazing scenery and conditions. We had a blast! 

I had my son at age 4 to both places.  Deer Valley's blues are in general steeper and wore him out more.  A lot of Park City's blues are quite accessible to most beginners.