either 3M command poster strips or string/wire and clips or binder clips and nails.

or use clip boards

I would do the string or you could do ribbon is you don't mind lacing ribbon through the cards.
I think ribbon would be really cute. Just punch 2 holes and thread the ribbon through, or you could just punch one and loop it through.

I hung cards like this in my son's nursery just a couple of months ago. I got the idea from Martha (where else?!) as seen here:
http://twostraightlines.typepad.com/two_straight_lines/2007/05/bedding.html

It's just bias tape with mini clothespins and it works pretty well. Mine are really thick, so each card has two clothespins, but you can make the tape stronger by putting the tacks closer together. You can see how mine turned out here:
http://www.flickr.com/photos/inkstainedwriter/2597962439/in/set-72157604121628803/

Hope that helps!

I use the 3M poster strips, like the first. 3M also makes some that have velcro on each side for hanging light pictures- those work great too. I have a whole series of the alphabet cards and number cards hanging up in our playroom for my son with these things- been up a year and half- look like the day I hung them! And my experience with the 3M strips is they really do come off without any harm at all to your wall (and I've moved quite a bit). One caveat- if the paint job on your wall really stinks, you may lose a few flakes when you take the strips off. Good luck!

Double-sided tape?

If they're truly lightweight and your wall is fairly flat, you might have good luck with that yellow tacky stuff everybody used in college to put posters up on the cinderblock dorm walls. I have no idea what that stuff is called, but you can find it in office supply stores easily, and about 60-70% of the time in Target. (I also use it at the bottom corners of things I hang on the wall with nails and hooks. It helps keep the pictures level so you don't get slanty pictures all the time!)

I've had good luck with the 3M Command stuff too, but I didn't know they made poster strips. That should work well!

You may want to try a Magnart Display system.
http://www.dickblick.com/zz573/26/

Reusable, doesn't detract from the art and doesn't damage it either. Could easily interchange artwork as well as your little one gets older.

Here's what it looks like in action:
http://dooce.com/dailystyle/2008/06/06_18_2008.jpg

i used the 3M command series sticky tab things for these exact cards (different print though). they stayed put for a good 3 years and came off with absolutely no damage. i used one sticky on the back upper left corner and one on the back bottom right corner.

all of these sound like good ideas...I want to know where the wonderful hardware alphabet cards are from!

Double Sided tape works well! I used it to hang those same cards! Good luck.

My MIL has taught elementary school for 25 years and swears by this. It doesn't damage paint (shocking!), lasts forever, sticks to anything (including brick), is cheap as dirt and simply peels off when done. No damage.

Hot Glue.

I know. Sounds insane. But it works!

I use glue dots for things that aren't too heavy. It never takes off paint either. I just put a crapload on. I also use the 3M strips and love those. I recently just put about 15 holes in my wall trying to get the hanging of the Family Tree frames from Red Envelope just right. I ended up using the 3M strips instead and hanging it up elsewhere to boot. I now have a whole wall I need to patch up and repaint. Oh, well, I guess you live and learn.

I used blue painters tape to do a test run on my daughter's alphabet cards and they've been up for 3 months - if it's not broke, don't fix it!

The yellow poster goo can actually damage your cards so I'd be careful of that. After a while it leaves a grease stain that bleeds right through to the front. Alternatively, but with the same basic functionality, you can use the white goo which is called Plastitak. That stuff doesn't leave grease marks. You have to knead it to warm it before sticking it, but it's pretty effective. I got some at www.classroomdirect.com, but I think if you look around you'd find it at office supply and teacher supply stores.

I was going to suggest 3M Command picture/poster hanging strips, but several others beat me to it!

Poster putty often leaves greasy marks on walls, and painter's tape is only intended to come off cleanly when used short-term.

The 3M Command Picture Hanging Strips are the best. They can hold pictures up to 10 lbs. But for lighter items like the cards you only need one strip. They are kind of like velcro but stronger. They are reattachable so you could rearrange the cards after you hang them up if you want.

My friends hubby works for 3M and suggested these amazing strips when I wanted a simple impermanent way to secure my lower kitchen cabinets. These work like a charm and my son can't get them open. When he is beyond babyproofing age they remove easily and won't damage my cupboards.

I tried double sided tape & it was a disaster but blue-tac worked a treat & no damage to the walls :-)

you can see my wall art in action in my kid's play room here

http://flickr.com/photos/pigeonpair/2593448837/in/set-72157605710921083/

fjorlief, Those are eeBoo Hardware Store alphabet cards
http://www.target.com/eeBoo-Hardware-Store-Alphabet-WC/dp/B0008236LK/sr=1-3/qid=1227147005/ref=sr_1_3/190-0110331-0148864?ie=UTF8&index=target&rh=k%3Aeeboo%20tools&page=1

I'm also a big fan of the eeBoo cards! I hung three strips of wide ribbon down the wall, and attached the cards with velcro dots. Worked great!

Thank you for all the great suggestions! I can't wait to see how they turn out.

My cousin got me these cards on Clearance at JCPenny. I believe they are available at the Land on Nod as well.