I have so many feelings about this topic, and I can't honestly say any of them are entirely objective.
There are many arguments for cutting and pasting other people's code into your application. Some of them may make sense, some may not. For instance, if you've got a method from someone's blog that takes an input and runs some complicated mathematical algorithm that's way outside your mathematical abilities and spits out a result - that's an argument for cutting and pasting - get the author's permission to use their code and credit them where due - it's the honorable thing to do.
There are arguments for not reinventing the wheel - again, this makes sense, in theory. But if you don't take the time to become intimately familiar with the code you're cutting and pasting, you don't know if there's a better way of solving this problem, you don't know if there are bugs in the code. What if the wheel you're pasting is broken?
There are arguments for speed and efficiency - you build up a library of other people's code that you've ripped off, stolen, plagiarized or otherwise, come to think of it, you may never even need to know how to program beyond Frankensteining some application together out of reclaimed parts.
There are times and places where I deem this behaviour completely acceptable. For hacking together quick throw-away tools that aren't designed for longevity but to get a task done, right now by hook or by crook. For the purpose of prototyping and studying concents, to learn and advance in a theoretical context I think this is completely fair game.
Cutting and pasting other people's code is plagiarism - if you have their blessing and you understand the code you're pasting and it fits within the construct of the coding standards for your application, then fine, I will concede it's fair game.
As a professional software engineer, I am being paid to maintain a standard and a code of ethics. I'm not being paid to steal, plagiarize or infringe on other people's copyright putting my client at risk of prosecution. Aside from this, there is a very real risk that when you run said cut/pasted code it has catastrophic side effects.
Not targeting this answer at you John, I know you're very ethically inclined when it comes to topics like this, so this is really just a general rant in the direction of the question itself.
Addendum: That said, I feel that cutting and pasting your own code between projects is quite acceptable - unless it was written as work-for-hire for someone else, in which case you don't own the copyright and you should get the permission of the person you coded it for. I've found that unless the code is pertinent to proprietry functional concepts, most employers are okay with you re-using your own ideas for other clients.