This site exists to do just what the name implies: provide a way for individuals (not businesses) to exchange postcards with other people around the world. It costs nothing to join, although if you want to donate to the upkeep of the site, you may.
Once you receive a Postcrossing member's address, you may read her/his profile. This gives you an idea of the person's interests and preferences for the type of postcard she/he would like to receive.
I derive a lot of pleasure from choosing a postcard that I hope will please the recipient. For example, I sent this postcard to a woman who has two small dogs on whom she dotes.
To see the variety of postcards that you can receive, take a look at my favorites, which I post at the end of each month on my personal blog at http://myturntodayyourstomorrow-cheryl.blogspot.com.