When should you think about changing your database schema?

Databases and their schemas, you know, they're always on my mind, especially when things get bigger. Schema changes can be a real headache, and nobody wants downtime. So, what's your best approach for moving those schemas around in a live production system? Are there tools or methods you really like, or maybe some you'd tell people to steer clear of? I'm looking for actual, useful tips. Thanks!