My hip sister requested that postcards be sent as invitations for her bridal shower. An eco-friendly idea since you eliminate the need for envelopes. Postcards are more casual than traditional card and envelope paper invitations, but a little more substantial (and practical if older guests are on the guestlist) than an electronic e-mailed invitation.
A few things to keep in mind when sending postcard invites. First, buy postcard stamps. It's a small savings, but it adds up. Second, you'll need to buy small labels to use for addressing them, unless you plan to handwrite all the invites. The side of the postcard reserved for the address is too large for regular mailing labels. You can print on regular labels and cut them to size, just be sure to measure the margins before printing so they'll fit on the postcard without any of the text being cut off. Third, have the postcards hand canceled. The postmark will go all the way across the top of the postcard and cover any text that you have at the top. Hand canceling is a small ink stamp that just covers the postage, without blocking any of your text. Many post offices will hand cancel for free; other post offices will charge 5 cents per postcard for this service. Finally, be sure to have the post office hand cancel in front of you. (I paid the 5 cents for 70+ postcards, only to find out that the post office did NOT hand cancel them after I left so make sure they do it while you are there.)