I have defined a custom field of type Integer Select. How can I import a list of integers into the dropdown options list (rather than enter them manually, one at a time)?
There are several extensions designed to do exactly this.
First is the aptly-named Option Values Importer. It hasn't been updated recently, and it only does the one thing - but it may be simpler to use as a consequence.
There's the configitems extension. This one has a bit more setup, but is great if you have to add/remove values on a regular basis.
Finally, there's the CSV API GUI extension. This is an alternative to the "API Explorer" approach Pete suggests, that lets you import in bulk from a CSV file. This works with all modern versions of CiviCRM and is probably the best bet if you don't want to mess with putting files into your web server's file system.
Is your motivation to transfer the configuration from test to production in a controlled way? A way to do this is to use the API that is part of CiviCRM. It contains a function Optionvalue for this purpose. The API can be called from PHP, drush or as a REST call. The best way to learn more is to use the API Explorer. You can find it via the following menu: Support -> Developer -> API explorer menu.
An example to add a soup to the Food preferences on the standard dataset is in PHP:
$result = civicrm_api3('OptionValue', 'create', array( 'sequential' => 1, 'option_group_id' => "soup_selection", 'label' => "Onion Soup", 'name' => "Onion_Soup", 'value' => "onion", 'weight' => 45, ));
Or directly with Drush:
drush cvapi OptionValue.create sequential=1 option_group_id="soup_selection" label="Onion Soup" name="Onion_Soup" value="onion" weight=45
Just to add to the options above. for brave (and knowledgable) souls who always take backups before operating on production (to paraphrase Dan's comment below) you can also do as an sql insert. For a few you can just 'copy as sql' an existing row then modify and run as a query eg
(93, 'Broth', 'broth', 'Broth', NULL, NULL, 0, 1, NULL, 0, 0, 1);
And if you have a lot to do I tend to do in a spreadsheet and use Concatenate and then insert.
Also a screenshot for the API Explorer approach