Match Eames Lounge Chair to a Lounge/Sofa  

Either:
A Florence Knoll sofa
or
a Poul Kjaerholm sofa
or
a Arne Jacobsen sofa
or
a Josef Hoffman Kubus sofa
or
a Le Corbusier Grand Comfort sofa

Skip
the Corbusier sofa and the Kubus sofa - both are the wrong period for the Eames, and both are a little too flashy.
IMO something simple and clean and comfortable as possible. Nick60 has a gorgeous Wegner sofa that would fit the bill. Personally I love his wood backed sofas, and I think the warmth with match the wood of the Eames. Knoll is a good choice too: you could do their Divina sofa. Olive and I own the Bensen Neo series, which is a great line - quiet and anonymous; comfortable and low. I've always been interested in Bensen's Canyon line too - which might bring the lounge a little more contemporary rather than MCM.
http://www.bensen.ca/

I saw the Corbusier sofa in black
sitting next to a Saarinen Womb chair and ottoman (at DWR), and believe me, it looked beautiful.
I have a couple of photos of a pair of Kubus sofas sitting in a modern setting with a Swan chair and a large Robsjohn-Gibbins Mesa table, a small Neguchi cyclone side table and a Nelson pedestal side table, and it looks classically modern.
It's perfectly OK to mix iconic pre-mid-century pieces such as the Barcelona chair, Kubus Sofa, and of the Eileen Gray pieces, Aalto bend wood chairs, or Corbusier chairs and sofa. All of these iconic 1920's and 1930's pieces still look surprisingly modern and appropriate.
right now, I have an Aalto Zebra fabric Tank chair in my living room and it looks perfectly cool next to my Knoll coffee table and across from my Baughman sofa.

Here is my Wegner sofa...
Here is my Wegner sofa (first pic) that LuciferSum kindly mentions above, I used to have a 670 and it looked great with the sofa. Florence Knoll sofas would work well, especially these two below..

Shouldn't there be one focal point?
It seems to me that the Eames lounge is a dominating piece of furniture and will be a focal point for the room. I wouldn't get a sofa that would compete with the Eames for attention, so I'd consider a simple cloth sofa over a leather sofa like the Corbusier. Maybe a FK or Wegner in cloth.
fm

Isn't that just a bit
too "interior decorator'? When I started to assemble my collection, I chose items that I liked and items I could find at reasonable prices, and all of my pieces looks real nice together.
Whatever happened to the pleasant surprise of finding cool pieces and discovering that they exactly fit together? I love the thrill of randomly grouping pieces together!

The prior message is just to illustrate
try to think "outside the box" and be open minded. For the most part, relative to the space you have, all "good" mid-century modern furniture looks good together, depending on what you like or don't like (I'm not fond of splayed legs, for example).

I understand what you're...
I understand what you're saying, but keep in mind I do exactly what you're saying you do...collect cool pieces of furniture and try them out together. Sometimes two iconic pieces do, indeed work well together, but more often than not, I've found that my place looked more like a DWR showroom than a residence if I put too many classic designs in the same space. I've tried pairing my Eames lounge with other black leather furniture and it was just too...overpowering.
That said, I also have a 5'7" black grand piano, which may be contributing to this perception. 🙂
In a spacious living area, I suppose it's quite possible to bring together iconic pieces done in similar materials and have a nice balance. It doesn't work in a smaller space like mine though.
fm

You're on the right track, FM...
Unassuming is the way to go.

Great, FM
That's the way to do it. Maybe I like a bit of clutter, but I'm satisfied with my living room pieces, and believe me, they were collected haphazardly!

My point
My point was more that something can be well designed, but not an "iconic" classic that screms for attention. Nicks Wegner sofa is beautiful...but *quiet*. Whereas I feel that the LC series is more of an attention getter all by itself.

Knoll sofa picture
Hi Nick -- I was wondering if you recall where you found that picture of the knoll sofa (the second, purple threee-seater with metal legs). I've inherited one from my grandmother, and it desperately needs reupholstering (a hack job in the 80s ruined it and changed the depth of the cushions). My grandma was certain it was Knoll, but since it isn't "THE" Florence Knoll sofa, it has been hard to find original pictures of it. I've been searching like mad so that I have something to show the reupholsterer. Any help much appreciated!
Thanks.

Pic comes from an old...
Pic comes from an old treadway catalog. There is only one picture. The link is below.
http://www.treadwaygallery.com/ONLINECATALOGS/MAY04/1001-1050.html

smartfurniture has 15% off Eames Lounge Chairs!!
Plus free shipping!A walnut chair w/o ottoman is $2561.,(and with Santos Pallisander is an additional $750.)I think the free shipping alone saves a bundle,as these usually cost a few hundred to ship.-Good luck!