Depends on the template/theme you are using. However the best place to start looking would be wp-content/themes/yourtheme/index.php In there you are probably looking for something like this: <?php the_time() ?> PHP:
Also depends on WHERE you're talking about, as the posts appear in the index, single post, category and archive pages (as well as search results). Like tflight said, you'll have to look for the code he posted in every template file it appears in.
I believe it's also located in post.php. Does anyone know what other files this the_time function occurs?
It'll depend on your own theme. Not all themes are configured the same. Mine, for example, handles all posts from the same file. You'll simply have to go through each file and search for that piece of code.
If you edit single.php, you will be able to remove dates from the posts. That's how i done, but i want to remove dates from the front page as well but so for no luck.