Beast's parents, Norton and Edna McCoy are still alive. Source, circa 2006
From the same source: Iceman and Nightcrawler.
However, it does seem that (predictably, as per Campbell's Hero's Journey) most of the main superhero parents are dead.
From that same Marvel thread:
cap - no (as in, not alive)
wasp - no
pym - not sure, assuming not
iron man - no
thor - no
reed - no
torch and sue - no
thing - no?
cyclops - no
jean - no
archangel - no
wolverine - no
colossus - no
storm - no
spidey - no
hulk - no
As far as the reasons, they are both archetypal, storytelling, and cultural.
Most of the mythological Greek heroes had effectively absent fathers, since they were all fathered by Zeus and he never took an active role in any of his kids' adventures. Moses was a foundling. Momotaro the Peach Boy of Japan and Ne Zha of China were spontaneous magical births, though Momotaro at least got adopted. Cinderella and Tarzan both had to grow up without their biological parents, though Tarzan ended up with a much better stepmother. That's cultural.
Archetypal - as per Campbell, a Hero's Journey must include learning to be on his own and rely on themselves. So parents have to go.
Storytelling - same reason really. You can get a lot more drama out of either having no family to talk to/rely on/be loved by, or by killing family off as part of a story.
Not really confined to superheroes:
Q: What about Harry's family - his grandparents - were they killed?
JK Rowling: No. This takes us into more mundane territory. As a writer, it was more interesting, plot-wise, if Harry was completely alone. So I rather ruthlessly disposed of his entire family apart from Aunt Petunia. I mean, James and Lily are massively important to the plot, of course, but the grandparents? No. And, because I do like my backstory: Petunia and Lily's parents, normal Muggle death.