Yes, if you purchase a custom design upgrade and do the required CSS editing you can hide the tags.
http://en.support.wordpress.com/custom-design/
http://en.support.wordpress.com/custom-design/editing-css/

MistyLook
To hide the category tags in posts note the following will also remove the comments link on the home page because the categories and comment link are all in one container in the HTML:
.post-info {
display: none;
}

Important note: CSS editing is theme dependent. In some themes, categories and/or tags cannot be hidden independently, as they are in the same selector as the other meta data elements such as author, date, and perhaps even the “leave a comment” link, which means if you hide one, then you hide them all.