The first science fiction magazine I ever saw, read, subscribed to, submitted to, and was rejected by was Isaac Asimov's Science Fiction Magazine. Back in 1983, when I was almost 16 years old, my father brought a copy home for me after it became clear to him that writing SF was just simply going to be something that I did, and there would be no use complaining about it. He found the magazine at a 7-Eleven and showed me the address for fiction submissions. It was a generous gesture on his part, especially since a few years earlier he had forbidden me to read the evil stuff.
That first issue had a Fred Pohl story on the cover, I recall, "The High Test." I read the magazine greedily, then called the phone number inside to subscribe. The woman on the other side of the line wanted me to give a credit card number. It took some doing, but I convinced her to enter my subscription without one, and to bill me later. I'm not sure why I didn't just mail in a subscription card. I think I was just too excited to get my subscription started.
Before long, I had my first rejection in hand—a photocopied sheet of possible reasons my story was not of use to Asimov's, with editor Shawna McCarthy's second-generation signature at the bottom. Crushed but undeterred, I sent in another story. Same outcome.
Every time the new issue arrived, I would read it cover to cover. Those pages are where I first read Lucius Shepard, Bruce Sterling, James Patrick Kelly, Kim Stanley Robinson, John Kessel, Michael Swanwick, Nancy Kress, Connie Willis, Michael Bishop, Norman Spinrad, Dan Simmons, and a host of other exemplary short fiction writers I'm forgetting now. I still have many of those issues, the ones with the stories that affected me most. "Speech Sounds" by Octavia Butler is one of the first that comes to mind. More even than the novels I had long read, those stories were my first real education in the art and craft of writing science fiction.

I would lie in bed some nights and picture myself in that company. I would picture my name on the cover of Asimov's.
Years went by. Editors changed. I kept writing and submitting stories. Eventually I started making sales—to other magazines. I made a lot. I even landed Shawna McCarthy as my agent and received a Nebula nod. And still that stack of Asimov's rejections got higher and higher. Something like 50 sheets high.
Then last year an email came from Sheila Williams, the newest Asimov's editor. She had received, read, and wanted to buy my novella "Inclination." The streak was officially broken.
Today BOGMONSTERasphalteden dropped by my office. He hand-carried me my contributor's copies of the April/May 2006 Asimov's, which should be available on newsstands early next week. (I do have the tremendous good fortune of working ridiculously close to the Dell Magazines offices.)
Twenty-three years later, my name is on the cover of Asimov's. I will admit to having to swallow a lump in my throat. I'm glad that young, starry-eyed kid is still around to see this—especially in an issue that Sheila describes in her editorial as coming-of-age–themed.