I don't think actual database independence is as important as the flexibility to be independent. That is, use as many database specific features as you can to spped up your program, but don't let that lock you into that database.

On the other hand, I don't think you should go so far into the database-independence religion that you make it impossible to get the most out of your database server (especially if you paid for all its fancy features). I know a lot of people like Class::DBI, but now that they use it, they're stuck with it. I think that can be bad too.