None. We have separate savings accounts but we both know what's in each others' and we effectively just use them like one big (actually quite little) pot, it's just that they're stored in 2 places.
I can understand having an emergency running away fund, especially if it's something you needed in the past, but I'd be quite upset if DH had £45k stashed away like a PP above and I imagine he'd feel the same. Barring abuse, I don't know why it would need to be a secret.
(Then again, that would be a life-changing amount of money for us right now (and at any point in our relationship so far) so perhaps it's relative and it'd be the equivalent of me having £5000 saved without his knowledge.)