If you use Firefox or Chrome as your main browser, here's a quick way of searching the Drupal API right from the browser address bar, without having to visit multiple pages to get what you're looking for.
Update: a big thanks to an anonymous commenter for explaining the Chrome equivalent to the Firefox method!
Of course, this works for any site, not just Drupal's API, but this is one of the lesser-known features of these browsers.
From the bookmarks menu, choose to Organise Bookmarks. Find where you want to put the bookmark (it doesn't really matter, since you won't be using the bookmarks folder structure to get to it) and add a new bookmark.
Enter any name you like, and in the Location field, enter: http://api.drupal.org/api/search/7/%s
In the keyword field, enter d7.
Once you've saved this, bring up a new tab in Firefox, and type, directly into the URL bar: d7 hook_theme. This will go straight to the API and search it for the Drupal 7 version of hook_theme().
You can set up a second bookmark for Drupal 6 if you need to, using the d6 keyword, or change the keyword to whatever you like. You can even set up searches for other sites. Just remember to replace the search part of the URL with %s. Have fun!
In Chrome, head to the spanner icon, then choose Preferences. On the Basics tab, click Manage Search Engines. If you've used the Drupal API before, it's likely that an entry is already there, so just edit it. If not, you can add a new one at the bottom.
Give the left field a label, then type your keyword in the middle field. You could use d7 as your keyword for the Drupal 7 API, for example. In the right field, enter http://api.drupal.org/api/search/7/%s.
Note there's no need to make the search into a default search unless you prefer it that way.
Come out of the preferences, and type, for example, d7 hook_theme into the URL bar. This will go staright to the API and search it for the Drupal 7 version of hook_theme(). Simples!