I love mid-century modern classics. Getting them can be a challenge if you're not a millionaire. To buy the "originals" you can look to Knoll, Herman Miller, The Republic of Fritz Hansen, or even Design Within Reach.
*Just to clear something up here: Knoll + Herman Miller + Fritz Hansen are furniture manufacturers. Many of these classic pieces were designed by designers for these companies, and they manufactured and distributed them. Design Within Reach is a retailer. The benefit of buying from DWR is they keep a lot of products in stock. If you order directly from the manufacturer however, you may have to wait longer to get the piece because they are custom made per order... but you can specify almost any fabric, finish, etc.
So back to getting these pieces. I found this website that has pretty decent reproductions of classic pieces for good prices. If you live in Los Angeles, you can even go to their warehouse in the Valley and pick it up. I did so for a couple pieces and recommend one of them here:
The Eames Molded Plywood Lounge Chair.
The one I bought is in a Walnut Veneer. If you were to purchase the original from Herman Miller it would cost almost $700, but the reproduction (which is quite good) was $230. Not bad for a classic piece that is considered to be "the most famous chair of the century."
This website also sells a reproduction of a coordinating Eames Molded Plywood Coffee Table. An original can run about $850 but Advanced Interior Designs sells a reproduction for $295.