What functionality of iOS can be accessed from the lock screen?

Solution 1:

I'm including the ones mentioned in your answer in the name of having a complete listing in one place.

• Toggle music controls (Play/Pause, Previous, Next, Volume) by double tapping the home button.
• Take pictures and videos by sliding the camera button.
• Invoke accessibility features by triple clicking the home button. Configurable in Settings-> General-> Accessibility-> Triple Click Home. You can configure toggling VoiceOver, toggling White on Black, toggling Zoom, or asking which to do.
• Make phone calls by tapping the Emergency Call button and dialing a number. iPhones only.
• View snippets of emails, text messages, and other notifications by looking at their notification preview. Configurable in Settings-> Notifications-> App.

• Activate Siri to make calls, send text messages, send emails, get directions, check calendars, etc. by holding down the home button. Configurable in Settings-> General-> Passcode Lock. iPhone 4S only.

• Take a screenshot by pressing the home button and sleep/wake button at the same time.

• Power the device off by holding down the sleep/wake button.

Solution 2:

Here's an older flowchart that gives a good overview of the home button features, and on the right side what you can do starting from the lock screen:

Solution 3:

Starting with iOS 5, the camera can be accessed from the lockscreen (obviously only on devices that have a camera). On iOS 5.0.x, double-clicking the home button reveals a camera button next to the unlock slider that can be clicked, and in iOS 5.1, there is a permanent camera button that you slide up to reveal the camera under the lockscreen.