If you are allergic to PHP, you could implement such a thing by editing your themes' cascading stylesheet. If you add "display: none;" to the following "taglist" elements, tags should only be displayed when you are logged in as administrator.
`.taglist ul {display: none;}
.taglist li {display: none;}
.taglist .tags_title {display: none;}`
You can either edit the existing elements in the .CSS file for your current theme, or just add the above code to the end of that file. I'm not certain, but I think an up side to this route would be that search engines would still be able to index the tags without them being displayed to a non-admin user. The down side is, if someone has CSS disabled in their browser the tags will still be displayed. I think this is a rarity nowadays, however.