You can NOT restore backups from a newer SQL version to an older - the formats of backup files are different.
From
http://msdn.microsoft.com/en-us/library/ms186858.aspx: "Backups created with Microsoft SQL Server cannot be restored to an earlier version of SQL Server"
So 2008 to 2005 won't work, nor 2008 R2 to 2008. If you try you will get errors like:
"The media family on device .. is incorrectly formed. SQL Server cannot process this media family"
or
"RESTORE HEADERONLY is terminating abnormally. (Microsoft SQL Server, Error: 3241)".
or
"The backup of the system database on device .. cannot be restored because it was created by a different version of the server"
Your options are:
1. upgrade the target SQL server to the same version as the source SQL server - this is the only long term solution. If you just need to restore once - see below.
2. use Import and Export Data Wizard (In SSMS right click on a database and select "Tasks > Export Data...")
3. use scripts (In SSMS right click on a database and select "Script Database as" or "Tasks > Generate scripts...")
Note that setting compatibility level on a source server to a lower setting won't help - it just affects the T-SQL, not how DB stored.
