> Another thought... if I'm tasked with maintaining or adding features to existing code, should I feel responsible for writing tests for the existing codebase?

Do you trust yourself enough to not break existing code while maintaining or adding features to it? What would be the consequence of you screwing up? Where would your screw up get noticed? Is it a scary person or group of people who will chase you down to fix it?

I've worked long enough to not trust myself at all anymore, regardless if it's old code or new. Then I evaluate according to above. Usually I land firmly in "yeah, better test it"-territory.