How to encrypt and decrypt a String in Apex using the Crypto class

The below wiki gives good set of examples for crypto classes

http://wiki.developerforce.com/page/Apex_Crypto_Class

A sample scenario from above article

// Generate an AES key for the purpose of this sample. 
// Normally this key should be stored in a protected custom setting 
// or an encrypted field on a custom object
Blob cryptoKey = Crypto.generateAesKey(256);

// Generate the data to be encrypted.
 Blob data = Blob.valueOf('Test data to encrypted');
// Encrypt the data and have Salesforce.com generate the initialization vector
Blob encryptedData = Crypto.encryptWithManagedIV('AES256', cryptoKey, data);
// Decrypt the data - the first 16 bytes contain the initialization vector
 Blob decryptedData = Crypto.decryptWithManagedIV('AES256', cryptoKey, encryptedData);

// Decode the decrypted data for subsequent use
 String decryptedDataString = decryptedData.toString();

Here is below blog that points a use case of how to store once we encrypt data in sfdc

http://cloudyworlds.blogspot.in/2014/01/encrypting-xml-response-from-external.html

Basically there are two versions

WithManagedIv()

Here SFDC itself handles vector generation

Encrypt()

Here one needs to include vector also as parameter for encryption.