Closest to I don't mind or I don't care?

Just to add to Chris' excellent answer, 

ça m'est égal  = I don't mind/it doesn't matter to me

but also

I don't care

in a very mild way.

For a stronger sentiment, you would use 

je m'en moque

Je m'en fiche

Je n'en ai rien à faire 

 je m'en fous

(which is not as vulgar as the translation might imply but generates an interesting  noun 'le je m'en foutisme' which is used to describe a couldn't care less attitude)

and a lot more expressions with various degrees of vulgarity which I won't go into now!

But an interesting question, nevertheless...