Can I Own This? I Wrote It!

I wonder about the ownership of what I write. Beshrew me, but I feel rather protective about what I write, not necessarily because it is wonderful, but because it comes from me. I mean the writing that involves real sweat, that takes me at least some hours from inception to finished product, which I sometimes send out and hear nothing about, or worse, which does get printed without my name attached to it.

Do I lose those pieces? Can they be picked up by anyone who wants, assuming someone wants?
Should I be flattered that someone wants to own them?

Should I be more grateful that a piece was chosen and worry less about it being credited to me?

I realise we live in the world of many blogs, in which a great deal of the written word is migrating to a brave new world to stand on its own merit. Does this suggest, then, that my concern is invalid and quixotic? I have been regularly contributing to a local South Asian magazine; the latest issue has my article in its entireity, but nowhere is my name mentioned. Even though I was told that I'd be given a letter head confirming that article as mine, there was a strong underlying tone of indulgent tolerance at my quaint disappointment, which, of course, makes me feel sheepish.
As the days have progressed, I have been feeling increasingly foolish, even though I am hurt enough to not want to contribute to that magazine again (knowing me, however, I probably shall).

I have been trying to come to terms with this situation. Library of Congress claims that I don't HAVE to slap copywrights on my work, right, left, and center, that the fact that I wrote it protects it enough. But I am still struggling: do I take my writing too seriously? Should I just post everything up and wean myself off the need to claim it as mine?

Maybe I should split up my writing into two kinds: the kind that's important for me to remain connected to, and the other to be offered up to the Universe because it is not serious enough. The former category would contain my almost-done book and poetry (that I have no idea how to market and publish, so they remain with me, like overgrown children).
The latter category would have my non-fiction articles and pieces like the short love-story I finished last night for a lark because my daughter always says I don't have a romantic bone in me and I wanted to prove her wrong (you may well ask who the adolescent is, here, but I won't wait around for the answer). I'd offer up this non-serious-for-a-lark writing up to the world and see if it spices up my blog, causes more hits, compels people to leave comments, etc.

Does writing then, need to outgrow its parent and break umbilical cords to be meaningful? If so, like children, can't it at least carry on its lineage? After all, what other insurance do I have against erasure?