Types of Action and Filter Hooks

The WordPress Codex has two important pages that can help you orient yourself with what hooks are available in WordPress.

NOTE: At the time of writing there is a bit of a transition of documentation on hooks from the Codex to the Code Reference site. Because of this you may find hooks that are listed on the Codex, but not documented. You should be able to find some documentation for all of the hooks if you search for them in the Code Reference, however, it does not have any current pages like the Codex where all hooks are grouped in one place.
The WordPress Action Reference page has available actions listed by the following categories:

• Actions Run During a Typical Request
• Actions Run During an Admin Page Request
• Post, Page, Attachment, and Category Actions (Admin)
• Comment, Ping, and Trackback Actions
• Blogroll Actions
• Feed Actions
• Template Actions
• Administrative Actions
• Dashboard “Right Now” Widget Actions

The Codex also has a similar Filter Reference page, which it lists by the following categories:

• Post, Page, and Attachment (Upload) Filters
• Comment, Trackback, and Ping Filters
• Category and Term Filters
• Link Filters
• Date and Time Filters
• Author and User Filters
• Blogroll Filters
• Blog Information and Option Filters
• General Text Filters
• Administrative Filters
• Rich Text Editor Filters
• Template Filters
• Registration & Login Filters
• Redirect/Rewrite Filters
• WP_Query Filters
• Media Filters
• Advanced WordPress Filters
• Widgets
• Admin Bar

Many of these filter hooks are separated into subcategories: Database Reads and Database Writes. This depends on whether you are reading from the database prior to displaying on a page or editing a screen, or you are writing code prior to saving data to the database.
Working with hooks in WordPress starts with figuring out what hook you need to tie your code into and then writing the code to modify the data you need or run whatever action you need.
If you get stuck or you are not sure which hook to use, you can usually figure it out by searching for something like: “WordPress action for [whatever you want to hook into].”  The WordPress StackExchange has a number of results with questions like this as well.