It is important to know what version a Drupal site is at before upgrading because it is good practice to download the current archive version of Drupal so that you can do a "code diff" with current site to determine which site files have been "customized" or changed. That way, you got a list of file changes that you might need to "code merge" the changes to upgraded version.
Note: This information refers to version 6.2 of Drupal, but may well be relevant for future versions as well.
There are a few ways of determining what version your current Drupal site is at.
The easiest way is to log into Drupal admin interface. Then go to "Administer -> Available Updates". It will tell you what version your Drupal core is at and if there is any updates availables.
In the root directory of your Drupal installation, you will normally find the file CHANGELOG.txt. If you look inside at the top of the file, you can determine the Drupal version. However, sometimes this file is missing or have been purposefully delete to avoid leaking Drupal information to outsiders.
Open up the file /modules/system/system.info and you will see something like ...
version = "6.2"
Here is more information about Drupal Versions in the Drupal documentation.
