My teens (15 and 14) have chosen not to have phones because they think that they lead to trouble. They both have laptops though, and no we don't have their passwords, never had (before they had their own machines they had profiles on the family Mac). I do have the passcodes for their ipods, and dd does use hers for messaging friends, but I've never felt the need to look.
When they were younger and more naive they were only able to use the computer in our living room so easily observable, plus the only time when dd got into a tricky situation online she came straight to us, and together we worked out a solution, composed statements to make, closed accounts, rang parents, went to school, talked to the school police liaison person etc (another kid was being bullied). She knows that we have her back regardless of whatever trouble she might get into, so we are fairly sure she will come to us if she needs help. Plus she is pretty robust online, refuses to be friends with people she doesn't really know and like, uses pseudonyms etc.
ds doesn't use social media really, just skype and steam when he is gaming, and he only talks about gaming so not terribly interesting.
They are both geeks and if they choose to do dodgy things they could do them perfectly easily without us knowing, and to be honest I am sure that they will. They've had lots of education about exposure, and as there have been two teen suicide deaths very widely publicised in the country where we live, and two older boys prosecuted for sharing pictures of semi-naked ex-girlfriends they are well aware of what can go wrong.