At first I was going to ask "Let's say Clark Kent has to die, what secret identity would you want to see Superman take on?" but then I ended up going more general instead:
I think the whole concept of a "secret identity" has become somewhat passe in this era of the government-funded or public-id character, but it's still a staple of the Big Names at DC and Marvel. You see a lot of reporter gigs, probably due to Superman's success, but it makes sense -- reporters get to set their own hours mostly, they have access to high-level sources of information in the government and police forces, and they can get into places most people can't. I never quite understood how Superman managed to keep the on-air job he held for a while, since if you have to dash off in the middle of a broadcast to fight a giant robot, that's pretty hard to miss.
Police officer comes to mind probably because I'm reading some of the classic original Blue Beetle stories, and he's a cop in them. But back in the Forties, being a policeman was a much different gig than it is now. I don't think it'd be as easy to just drop your uniform and run off in tights to fight crime; the first thing your boss would want to know is where the hell "you" were during the whole thing, you know? Being there and visible is sort of part of the job.
A P.I. has lots of interesting possibilities, depending on your power set. You get a lot of the perks of being a cop without a lot of the red tape. And you have a good "in" for cases to take on.
Politicians apparently have scads of free time where they can run off to various locations, but the media is always going to be all up in your bidness, so keeping your alternative lifestyle would be a real chore.
I threw "scientist" in there as a nod to Barry Allen, the original Flash, but come on -- burying yourself in a lab all day is not exactly the way to stay current on the reigning underworld boss, you know?
Finally, I think my favorite one is "janitor". No one ever notices the janitor, and if you worked in the right place and had the right power set, you could get a lot of fantastic information without anyone being the wiser.
Which job would you choose?