Drupal - Using IN clause in db_query

You are missing the braces.

Try this:

$nids = array(1, 2, 3);
$result = db_query('SELECT * FROM {node} WHERE nid IN (:nids)', array(':nids' => $nids));

For more information, see http://drupal.org/node/310072, especially the chapter on Placeholder arrays:

Placeholder arrays

Drupal's database layer includes an extra feature of placeholders. If the value passed in for a placeholder is an array, it will be automatically expanded into a comma separated list as will the corresponding placeholder. That means developers do not need to worry about counting how many placeholders they will need.

An example should make this behavior clearer:

<?php
// This code:
db_query("SELECT * FROM {node} WHERE nid IN (:nids)", array(':nids' => array(13, 42, 144));

// Will get turned into this prepared statement equivalent automatically:
db_query("SELECT * FROM {node} WHERE nid IN (:nids_1, :nids_2, :nids_3)", array(
  ':nids_1' => 13, 
  ':nids_2' => 42, 
  ':nids_3' => 144,
));

// Which is equivalent to the following literal query:
db_query("SELECT * FROM {node} WHERE nid IN (13, 42, 144)");
?>

For Drupal 8

Entity query:

$query = \Drupal::entityTypeManager()->getStorage('entity_type')->getQuery();
$query->condition('field/property', [1, 2, 3], 'IN');
$ids = $query->execute();

Sql Query (select), essentially the same for other query types.

$query = \Drupal::database()->select('table', 't');
$query->condition('column', [1, 2, 3], 'IN');
...

For Drupal 7

See Berdir's answer.

For Drupal 6

You can do it like this:

$nids = array(1, 2, 3);
$placeholders = db_placeholders($nids);
$result = db_query("SELECT * FROM {node} WHERE nid IN ($placeholders)", $nids);

db_placeholders is needed in Drupal 6 which will creating a string that holds the placeholders needed for the array of values given. Drupal 7 handles all this internally like Berdir describes.

Using the Database API in Drupal 7

Here's how you can use db_select() instead of db_query() for the same results.

$nids = array(1, 2, 3);
$query = db_select('node', 'n')
  ->fields('n')
  ->condition('n.nid', $nids, 'IN')
  ->execute();
$nodes = $query->fetchAll();