I think for me, the most sure-fire appealing SF is that which deals with questions of identity.
Blade Runner is the most obvious example of this: Androids (Basically) are programmed with false memories of their lives prior to their activation for psychological reasons, but they know they're androids. A detecive is hired to track them down. Along the way he meets another android who doesn't know she's an android because of the fake memories, and handles it not at all well. In the end, after killing off the last of the bad androids, he discovers that he's an android, too, and runs.
Dark City is another one: a guy wakes up with Amnesia, framed for a murder he may or may not have committed. He's got an estranged wife that he loves, and is on the run, but he notices that the map of the city redraws itself every night, and he ke keeps seeing the same people in different jobs every night, and begins to suspect that he's never even met his wife prior to visiting the movie, that those are false memories. As it turns out, a hive-minded alien species is trying to find "The Human Soul," for lack of a better word, and have been trying to find it by redefining people's lives and memories dozens of times, assuming that which doesn't change is the thing they're looking for.
The Prisoner TV series spends 17 episodes with a character named "#6" attempting to figure out who the shadowy ruler of The Village, "# 1," is. Ultimately it turns that it is and has always been #6 himself. (And in fact, they told us that in the opening titles of every episode: #6 says "Who is number one?" and the #2 of the week says "You are number six." Which actually is written, "You are, number six.")
Much, if not most of Philip K. Dick's novels and stories touch on this to some extent. The most notable case is in "A Scanner Darkly," when undercover narc Bob Arctor is accidentally asigned the task of spying on himself by mistake. Rather than blow his cover (Even his bosses don't know who he is), he goes along with it, and gradually suffers brain damage to the point where he's Bob half the time, and a druggie the rest of the time. the ultimate attempt to re-fuse his identities devestates him, and turns him in to yet another person, who's just another burned out wasteoid.
There's a book - forget the title - where the main character is a spy who's memory is wiped after every mission. He then has it put back in at the start of his next mission, and he's always quite shocked to find out all the stuff he's done.
I like hard SF, but I don't see this as incompatable with that. I also like questions of the human soul, and this is all about that.
In the end, I suppose, a line from one of Laurie Anderson's songs has always stuck with me:
"We don't know where we come from, and we don't know what we are."
SF is uniquely suited to try to define the parameters of that question, even if it is fundamentally unanswerable. I admire anyone who takes a stab at it.