Yes. Use a shared user table:
http://codex.wordpress.org/Editing_wp-config.php#Custom_User_and_Usermeta_Tables
You should make one site the 'main' site. Then, whenever you make a new site, use the same database, but CHANGE THE PREFIX for each one. Then, define CUSTOM_USER_TABLE and CUSTOM_USER_META_TABLE in wp-config.php so that it looks at your 'main' site's user tables. For example, say your main site is set with a database prefix of site1_, you would then, for site2_, add this to the wp-config.php file:
define( 'CUSTOM_USER_TABLE', 'site1_users' );
define( 'CUSTOM_USER_META_TABLE', 'site1_usermeta' );