What about those plexi photo blocks? You could only display one at a time that way though, but you could rotate your collection and that would allow you to see both sides.

Find a glassine envelope or sleeve that fits a card, perhaps online for baseball cards, etc. Then place an office style clip on the top and hang them using clear push pins on whatever background you choose, in three rows of six. Then the card can pe tahen down and reversed to access the back.

I think one of the picture frames that "floats" a photo between two pieces of glass would work fantastic, particularly if you have a pass-through or somewhere you could hang it as a sort of wall divider. Then you could admire both sides. May I suggest doing every other card flipped so you get a checker board of fronts and backs? It would make it visually interesting even more so than they already are. What a great find!

How about a mobile like the one with characters from "The Wire" on Amy's Salvaged Sanctuary in the Sky house tour:

Close-up View

Wide Shot

The pictures are not framed, but this way you could see them both ways.

Urban Outfitters has an affordable mobile that might work.

And so does Amazon.

I'm sure you can find other examples if you wanted to go this route.

You could buy or make one or more hanging mobiles designed for small photos and use your cards instead of photos. Depending on the design, both sides of all of the cards could be visible as the mobile or mobiles shift in the air. My husband bought a couple manufactured by www.kikkerland.com a few years ago.

P.S. You could put the cards in archival-quality clear pockets made for photos and then attach the mobile clips to the tops of the pockets rather than directly to the cards.

P.P.S. Or, you could make high quality photocopies of the printed backs of the cards and display a photocopy next to the front of its card in a framed arrangement.

for some reason, i'm seeing some possibility of building a diy room divider...with plexiglass or something. almost like a french door concept with dividers so each one is individually framed.

i have NO idea how this would work, but i'm picturing it being awesome!

I've seen similar-sounding room dividers that were designed to display back-to-back-photos. A DIY divider could be unique, striking, and useful.

Seal the cards between two pieces of thick glass or plastic and you've got 18 great coasters!

I'm excited about the room divider and mobile ideas. I also have a set of these tobacco cards and have been mulling over how to display them. Maybe you could thread a thin piece of fishing wire through them - link the top of one card to the bottom of another, and so on.

My mom and I actually both inherited a big collection of these cards, and we went with the "floating" frames, ensuring of course that they had archival quality glass...these cards fade FAST if you leave them in light unprotected, so as much as a lot of these ideas sound super fun and really creative, please make sure that any materials you use will help hold up the cards for years to come. Eventually they could pay for someone's college education!

I like the mobile idea.

A cheap alternative would simply be to carve a thin channel down a nice long piece of hardwood and stick them in it like placecards.

Along the lines of what has already been suggested, this frame I saw at Pier 1 came to mind:

http://www.pier1.com/Catalog/HomeAccentsD%C3%A9cor/HomeAccentsD%C3%A9cor/tabid/508/CategoryID/134/List/0/catpageindex/12/Level/a/ProductID/1566/ProductName/9-Clip-Window-Wall-Frame/Default.aspx

Same idea could be executed on the cheap if you DIY.

I have a set of Japanese comic postcards that are similar in shapes. I used blue poster hanging goo to hang them in rows in my kitchen. Looks great, and none of them have fallen.

I think I have seen specialty collector frames for baseball cards (if they are the same size) in frame shops and places like Michael's Crafts... Might be worth a look or phone call...

http://www.cigarettecards.co.uk/frames.htm

Some cigarette cards can be worth quite a bit. Be sure to protect them!