If you use the Pathauto module, you can set an automatic alias for the user profiles using a token that is replaced with the username. In Pathauto for Drupal 7, the default pattern for user paths is /users/[user:name], which is the pattern I would suggest to use to avoid conflict with path defined from other module. As you don't control the username chosen from a user, it could happen the username is admin, which conflict with the path used from system.module for its own menu callback.
If you want to use a different token, the list of available tokens is available right after the text field used for the pattern to use.
What I reported is still valid for Drupal 6; the difference is that the token for the username is [user].