What line are these George Nelson pieces from?  

Believe the metal handled...
Believe the metal handled pieces are called the Primavera line. I've never seen the cabinet with the glass and wicker, but it's not Nelson methinks...

Those Thin Edge cabinets
fit on the slat bench.

?
Am I missing some pics? I dont see any thin edge pieces in the 5 pics I see.

Ok, make it "Those cabinets...
Ok, make it "Those cabinets with the Thin Edge pulls fit on the slat bench."

Dammit.
And now I see that the pulls aren't Thin Edge. Sigh...
In any case, the cabinets seem close enough to the right size that they'd fit on a Nelson slat bench.

I don't see
any pictures.

Same here Barry.
Same here Barry.

Jeremiah
The pieces are ~50-60 years old, no specific "line", kind of rare although those legs are not as desirable as other choices. Primavera is a color option, not a line. the handles are great, "wave" pulls.

Basic Cabinet Series
These are from the "Basic Cabinet Series" and from the photos I'd guess they are walnut. Primavera was one of the veneer options, but it is more blond and has a flame-like grain.
The cabinets were designed to be used with one of the leg options or to be supported by a slat bench. They could also be hung on the wall. If yours were originally sold with a bench, it may have a couple wide strips of felt on the bottom. Your cabinets are probably just over 56" wide which means that if you want benches to put them on, you'll have to find vintage. They don't make that size bench any longer. A walnut cabinet looks great on a black bench.
I don't think the cane-front doors are original. I've never seen one with that kind of door and the pull, hinges, and corner joinery look wrong. They appear to me to be added on or altered. They offered that asymmetrical form with a solid door, but the hinge was largely concealed.
If your dresser and single door cabinet (with the X pull) have two rectangular marks on one edge of the top of each piece, there was originally a suspended vanity between them.
This line was in production for a number of years. If there is a label on yours, that would help date them. Most likely it will have a rectangular silver label. It will either be paper with square corners, or stamped metal foil with rounded corners.
Basic cabinet group is probably the most common of the Nelson case goods followed by the steel-frame group. The rosewood "thin-edge" group is the hardest to find, the most sought after, and most valuable.

label
here's the label. only 2 pieces are marked.
also, Pegboard Modern, do you think the long 2 piece unit is definitely a herman miller piece, just with some later modifications?
and, would $2000 be a fair price to ask for the set?

Yup, they're
Basic Cabinets in Primavera. They're beautiful and if you don't want 'em, send 'em right here!

Perhaps Jeremiah
There are a number of variables regarding price. Of course no matter where you sell it, condition is important. It looks to be in fair overall condition except the night-stands which clearly have water damage on the tops.
The context in which you sell it has a lot to do with the price you will get. You can ask anything, what you will get is another story. Craigslist buyers have a certain price expectation, eBay buyers another. If you can get a reputable auction house to sell it, you might realize a better price, but you will of course have to give them a commission.
You location can even make a difference. If you are selling locally, the relative demand and the local market can vary greatly. If you are not in an area that has a strong market for mid-century, you have to factor in shipping and the associated cost.
I think $2000 is a reasonable starting point. However, I'd be open to good offers. The most desirable pieces will probably be the dresser and the single door cabinet. They are in pretty good shape and are nice useable things. The glass-front cabinets are nice, but need something to make them useable (a cleat to hang them on the wall, a bench or some legs) plus, as I mentioned, I don;t think the cane doors are correct. The two night-stands wold be much more desirable if the condition was better. If you want to get the best price, it might be worth investing in having them refinished.
The label is the earlier paper version and would date the piece to around 1950- 1952.
Good luck.

Walnut
I'm fairly certain those are walnut Barry. These are primavera. Poor photos, but as you can see the color is much lighter and the grain pattern different.
If Jeremiah's look light in his pictures, it's probably because of the direct sunlight. Look at the photo of them stacked in the garage.

I'm confused, Jeremiah...
Why do you come here for advice if you're going to ignore it?
http://cgi.ebay.com/George-Nelson-for-Herman-Miller-Dresser-eames-era_W0...
http://cgi.ebay.com/George-Nelson-for-Herman-Miller-1-Door-Cabinet-eames...
http://cgi.ebay.com/Pair-George-Nelson-for-Herman-Miller-Side-Tables-eam...