Ha yes, you're absolutely right. It all depends on the person being introduced, since no one anime will please everyone.
I'm glad to see I'm not the only one who feels that way about Cowboy Bebop. I don't know if it was just me or if the fans made my expectations too high, but it's obvious I missed something. The soundtrack was the best I've ever heard, though.
And Black Lagoon. I was really into the first few episodes, having never seen an anime with so much action that kept me on the edge of my seat. Once the novelty wore off by the end of the season, I realized that there wasn't much behind it. The characters were unlikeable, the story was so uninteresting it might as well have been nonexistent, the soundtrack was bland, and the show went on for far too long, not having enough substance to justify the length. I also watched the dub, which I think was a mistake (the actors were fine, but they overused swearing more than Elfen Lied overused nudity, to the point of being ridiculous). This was all IMO, of course, and I hope that somewhat clears it up for you.