If I have two instances of Sql Server 2008 R2. One is standard edition, one is web edition.
If I take a backup of a database from the standard instance can I restore it to the web edition instance?
As long as the version is the same ("SQL Server 2008 R2"), you can restore back and forth between the two servers however you like. The edition ("Standard", "Enterprise", "Web", "Developer") of the source and target will not matter.
One thing to watch out for is file placement. If the driver lettering is different on the servers or if paths are not quite the same, you may have to tell SQL Server where to put the files. Otherwise, the restore should pretty much just work.