The site linked to your username, http://www.borgstijn.nl/ , is not a wordpress.com site. If you are talking about that site, we cannot help you.
If you are talking about a site hosted here at wordpress.com, then we need a link to it.
At wordpress.com, and in blogs in general, posts are organized by date, so there is typically always a date shown. In some themes, the date can be hidden by CSS if you have the Custom Design Upgrade, but this is not the case with all themes. It just depends on how the theme designer organized the markup (XHTML) and the CSS.
This CSS would get rid of the date on the theme you currently have active on your site, but you would have to have the Custom Design Upgrade.
You can go to appearance > custom design > CSS and paste this into the CSS edit window and then click the preview button to see the change. With some browsers you may have to force refresh the browser to see the change.