Students should learn not to plagiarize for a different reason: citations generally make a paper give a more favorable first impression. Obviously, if the prof gets suspicious and starts checking those citations and they don't say anything remotely resembling what you're saying they say, that will hurt. However, in most academic settings, citations help much more than they hurt.
In most professional arenas, things are indeed different. Stopping to say "as once said by {AUTHOR} in {WORK} ...." when giving a speech to a broad audience is awkward and often doesn't make your speech that much more credible. In fact, it can give it a whiff of insincerity by giving the counterproductive impression to your audience that you're hiding behind some important-sounding names that they've never heard of. Even names that are household names to the chattering classes (e.g., Milton Friedman, Joseph Stiglitz) aren't exactly known much more widely than your average MLB player (and that may be being overly charitable).
On the Web, however, particularly in the blogosphere, plagiarism without a link remains a serious issue because of financial implications, modest though they may be in the grander scheme of things. Linking to your sources is important because it may drive some measure of traffic, however small, to the originating site. Those page views are important. In addition, linking to one's sources does not disrupt the flow of one's speech or otherwise stylistically hamper one's argument on the Internet.