This is a good idea. I do postcards a lot. Sometimes it's because there are so many groups I want to help that I ask for a name & the box just doesn't get done due to lack of funds & time, so at least a postcard goes & sometimes monthly postcards. Other groups I'd really like to support but have small numbers & many requests for their addresses, so I do the same.
Also when we have family & holiday picnics, I get out the postcard supply & the anysoldier notebook & have everyone pick a contact & write a postcard. For the neighbor's birthday, I pulled out only the marine contacts to choose from in order to honor his service in the corps.
Sometimes I send a group of postcards in a package to 1 contact & ask him/her to distribute them, especially if they say they forward stuff to outlying posts or to people who aren't getting mail. Some of our most consistent penpals have come to us that way. Recently at a rock & gem show I picked up a bunch of small, pretty, smoothed rocks to be included in a baggy with the postcard to do that, & explain that the rock is something tangible they can carry if they want, to remind them that someone stateside is thinking of them. (Even tho sending rocks to Iraq sounds inane. Waldenbooks used to carry a kids' rock-painting kit that always tried to lure me into sending it to Iraq.)
Postcards are quick & I can write one during breakfast. They're also easy to carry for those times when you're waiting for 10 minutes here or there for someone. I do put my name & address in tiny letters across the top & haven't had any come back.
A cheap way to do postcards is buy 4x6 blank index cards & stickers. I often use those for return cards in my boxes (with a note that if they can drop it in the mail, we'll know they got the box, followed by a smiley & their name so we know who it came from). Or draw on them freehand or use stencils or, as someone else suggested, stamp on them. We also keep our eye out for special deals & good prices. We buy a lot at a Ben Franklin store (also really nice $1 5x7 notecards there!) & pick them up at rummage sales & good will type places. A local Boy Scout troop always has masses of them at their annual rummage sale & last year they gave me a huge discount when I told them the postcards were for deployed troops.