Yes, you need to purchase exactly the same license on both ASA if you are running failover, and running ASA version 8.2 and below.
However if you are running ASA version 8.3 and above, no, you do not need to purchase 2 license for ASA running in Active/Standby failover. You can just purchase 1 on the Primary firewall, and it will work when it fails over.
Here is more information on licensing on version 8.3 and above for your reference:
http://www.cisco.com/en/US/docs/security/asa/asa83/license_standalone/license_management/license.html
If you decide to upgrade to version 8.3 or above, please check the memory requirement as well as all the new features (especially NAT that has completely change from version 8.3 onwards).
Hope this helps.