Node Field module allows you to add custom extra fields to single Drupal nodes.
It's not connected to fields module, so different nodes of one content type can have absolutely different sets of custom fields.

You can add text fields, long text fields, links, taxonomy fields, radios and selects.
You can use date fields, if you activate date and date_popup module (http://drupal.org/project/date).

Installation

Install Node field module
Go to admin/config/node-field. Select node types to use node field module
Now you can add unique custom extra fields to your nodes!

UI is made the same way as in fields module. Many hooks were added, so now it can be used as a base for more complex modules.
You can add new node field types using hook_node_field_info_alter. You can change fields widgets and formatters. And so on!

There is an extended version of this module now called Sky field (http://drupal.org/project/skyfield). It's quite the same but provides a wider functionality and flexibility, because it works with any drupal entity, not just nodes! Please, use it and help testing it.