I guess lots of people don't fear death because it seems so far away you can ignore it. Moreover you can't avoid it. It's more useful (genetically speaking) to program a fear of spiders or heights or a crowd surrounding you (barbaric enemies, on the scale of genetic evolution the "memory" of barbaric enemies is a very recent one), because that could make you avoid possibly dangerous things that CAN be avoided. Which is genetically useful because it will improve your chances to reproduce. Remember any gene which improves the chance of itself being copied will be "rewarded" by lots of copies and thus survive.
On a more personal level: I'm quite afraid of death, but I'm able to put that fear away and rationalize it. I can think about death, feel very afraid, and the next moment think about something else and make the fear go away. Which is not the case for some other fears of mine. In such a survey I'd put those before death.
I'm afraid because it means the end. After death I can't finish my novel, so I've got to finish it NOW. Same for any other plans (read: mad ideas). Which are, of course, too numerous to count, let alone realise them! My image of death is a bunch of unfinished projects being thrown away. Or worse: being kept "because they are mum's (...)" but with no intention of ever finishing them or displaying them, and with complaints of them taking up too much place...