Not all phones can do this, but most Android phones can. By now, you know that encryption is the process of locking data with a key such that (when done right) even serious adversaries cannot unlock it. You can encrypt data for transit (such as when you view a Web site over HTTPS), and you can encrypt data for storage. The latter protects your data in the event your device is stolen (or “seized”).
For most Android phones, this is trivial: simply go into Settings -> Security, and there will be an Encrypt option. You may need to encrypt your phone and SD card separately, and you’ll need to set a strong password on your phone (no more 4-digit PIN, sorry!). iPhone users are a bit out of luck on this one: even with a PIN lock, someone with the right tools can grab your data, and there’s no real encryption option. Perhaps you could instruct Siri to delete your stuff if someone kidnaps her! 😉
This is one of a 30-part series, “No Surveillance State Month,” where daily for the month of June I’ll be posting ways to avoid invasion of your privacy in the digital age. The intent of these posts is not to enable one to escape detection while engaging in criminal activity — there’s still the old-fashioned “send a detective to watch you” for which these posts will not help. Rather, this series will help you to opt-out of the en masse collection of data by the government and large corporations that places Americans in databases without their knowing and freely-given consent for indefinite time periods. We all have the right to privacy, and I hope you demand it.
Professional Troublemaker ® 
I beg to differ.
Every iPhone since the iPhone 4 has an integrated encryption chip that encrypts it’s contents automatically using AES-256, whether you want it to or not. The only way to decrypt the data is to defeat the password. If you’re using a 4 digit pin code or an easy to guess password, then your data can be easily accessed, it’s pretty much impossible if your passphrase is impossible to guess.
Also, remember to check the “encrypt iTunes backups” on your computer, other wise, regardless of how complex your passphrase is, your data will not be protected.
iPhone may automatically encrypt, but the problem lies in that the key is on the device, and is weakly protected. Although this is useful for providing some protection to your data, I wouldn’t imagine the NSA would have a hard time hacking it. See: http://www.eweek.com/c/a/Security/iPhone-4-Encryption-Remains-Uncracked-But-Password-Keys-Easy-to-Obtain-686228/