Unlock a record which is locked by approval process

As of Winter '16, this is now possible through APEX. (Release Notes)

It can be enabled by going to Setup > Create > Workflow & Approvals > Process Automation Settings :

EDITOR NOTE

As mentioned in other answers, this feature is now possible out of the box as of Winter '16.

Original Answer

not out of the box.

What we did in a client project was:

1. Create RecordLockStatus__c picklist field with valuess [UNLOCKED, IN_APPROVAL, LOCKED]
2. Create UnlockToken__c text field
3. Create an approval process with entry criteria RecordLockStatus__c='LOCKED' and UnlockToken__c = ?SEMI_SECRET_TOKEN? to prevent accidental unlock and sets RecordLockStatus__c='UNLOCKED' and UnlockToken__c=NULL. Make sure to set the approval's order to 1.
4. For all your other approvals make sure that you set RecordLockStatus__c= 'IN_APPROVAL' when entering the approval and RecordLockStatus__c='LOCKED' when locking the record on finish
5. To unlock your record query it (make sure RecordLockStatus__c='LOCKED') and submit for approval using Apex http://www.salesforce.com/us/developer/docs/apexcode/index_Left.htm#StartTopic=Content/apex_process.htm

hope that helps