ping inside "ip address at the other end of the tunnel"
Inside interface will have to be in the encryption domain.
This requires that the management-interface command is set to the inside interface - like "management-interface inside".
Let's say you have a bunch of interface mappings in your VPN tunnel to the other end. To test each of them do the following - if you want to test as an example from the dmz interface
ping dmz a.b.c.d
where a.b.c.d is on the other end of the tunnel end-point.
Tested on an ASA v.8.3 to ASA 8.2.
By the way, if you have multiple network mappings in the same crypto acl, don't use set reverse-route on the crypto map entry. This may cause issues with the way the ASA uses the crypto ACL to create new tunnel mappings.