My understanding is that separation anxiety is a developmental milestone that occurs when the child comprehends that s/he and mama are two separate people -- which means mama can leave, and this can be scary. But I agree with pp that the severity has a lot to do with personality. My dd is 10 months, is very outgoing, and shows no signs of it whatsoever. I asked a psychologist who specializes in children, and she said it really varies from child to child, although she did say secure attachment "might" ease things, although not necessarily (it certainly won't hurt things). There's a large continuum of "normal", so one child may have a very mild "case", whereas another may be scared and clingy for quite some time. Or anywhere in between!
ETA: Just to clarify, dd won't just go to anyone. She doesn't like my mom very much, for example, and is always a little reluctant when my mom holds her, and sometimes cries. I don't consider that separation / stranger anxiety, though. My mom is a really messed up person, and doesn't respect my dd, is rough with her, takes her toys away unexpectedly, etc. (and as a result is never left alone with her and sees very little of dd). So I feel that dd's reaction is perfectly legitimate. And she can be a bit tentative around new people for a little while, but I wouldn't like it if someone I'd never met walked over and picked me up either, lol, so I also don't consider that stranger anxiety. OTOH, I went for my yearly pap yesterday and set her on the floor while they were weighing me. When I turned around, she was headed down the hall and around the corner, lol. So in general, she has very little fear of new places or new people.
Mama to M (7/05) and S (5/08) my surprise !!!