Can CiviCRM work by itself (e.g. without Drupal)?
There is a paid service you can use for this, if you wish to go that route:
CiviDesk offers a hosted standalone version of CiviCRM you can subscribe to.  Nicolas from CiviDesk has expressed interest in other people using standalone Civi, so you may want to talk to him. You can download the code for standalone Civi here, but of course this isn't supported by the core team.