There are multiple possibilities, depending on want you want.
Overridable settings
You can use variable_get('your_module_your_key', $default_value);
. Then, it is easy to override that either in settings.php with $conf['your_module_your_key'] = 'other value';
. See http://api.drupal.org/api/drupal/includes--bootstrap.inc/function/variable_get.
It is also easy to build a settings form for that, see for example http://api.drupal.org/api/drupal/modules--menu--menu.admin.inc/function/menu_configure/7.
Note that you should always prefix your variables with your module name and that you don't use this for variables that change frequently because every change results in a cache clear for all variables. Also note that all variables are loaded on every page request, so don't create too many of them or store big data structures in it. They are mainly meant for configuration.
Static get/set functions
You can write simple get/set functions which use a static internally to exchange variables during a single page request. See for example http://api.drupal.org/api/drupal/includes--path.inc/function/drupal_set_title/6.
Keep in mind that these things are only kept for a single page request. Here is an example implementation which allows to save multiple variables identified by a string and therefor works similar like variable_get()/set().
<?php
function yourmodule_static($key, $value = NULL) {
static $storage;
if (isset($value)) {
$storage[$key] = $value;
}
return $storage[$key];
}
// Then, you can use it like this:
your_module_static('key', $value);
// And then in a different function/file:
$value = your_module_static('key');
You could also extend it to return per reference and so on.
Cache
To store for example data from slow database queries or complex calculations, you can use the cache system. http://www.lullabot.com/articles/a-beginners-guide-to-caching-data looks like a detailed and great explanation of that.
Note that the cache is stored in the database by default but is pluggable and can for example also use APC or Memcached.