I'm currently building a web application in Ruby on Rails. Is it safe to store billing/postal addresses in a database?
What could happen if the data were compromised?
Are there any standard practices to make this data more secure?
On the fundamental front, it is never secure to store or transmit anything somebody wouldn't want people to get. You can make things safer by using various security/encryption methods, but it is still fundamentally unsafe.
On the practical front, addresses are so easy to get as it is. You should avoid correlating them to more personal information which is not a matter of public record, like credit card numbers, social security numbers, passwords, etc.
I believe most users would be as irritated by having to continuously re-enter their address as they would having their addresses lost in a compromise - but one of those makes them think you're making their life harder and one sounds like "a thing that just happens."