Here's one of the safest way to weird people out: Go to any public place (let's say a bar, a club, a bus stop, the cafeteria) and announce that you like poetry. Then enjoy the reactions.
Most people think poetry is terribly obscure, even opaque, and they don't know what to do with it. Consequently, they say they hate it. But, as with many things, they hate something they don't understand. Not because they're too dumb to understand it (it's quite easy, actually), but because they haven't tried.
This is a shame, frankly. The basic elements of poetics are so frequently employed in political, social, and business rhetoric that we don't even notice it anymore. And the poetic principles can teach us many things about how language and information is structured and may be presented. I'll try to be lucid.
But why may this article be relevant to content strategists, information architects and copywriters alike? Because we essentially do very similar things and oftentimes take care of work not primarily affiliated with our field. Also, there's no harm in being firm in all disciplines concerning communication. That does not mean you should write Petrarchan sonnets or include a limerick in every paragraph you write. It just means you should know a little more about how language and communication works in order to use this knowledge to your advantage.

Anyway, if you're working in a web environment, chances are you have been in need to write some copy. And even the ones who feel they haven't, either have done so unnoticed, or at least should have done. (On a side note, I'd like to refer you to the great article by Jason Fried: "Why most copywriting on the web sucks")
No matter if it's your G+ or Facebook profile or a CV, an app you want to present, information on a website you're designing, or email contact with a customer: All of these writing activities (and a lot more) contain some elements of copywriting. And, as I will argue, poetry.

1. Form

The first important thing is that the form should always, to a certain extent, refer to content – in regard to theme, style, and representation. So, when organizing content, you should (and maybe you do intuitively) match your content to your form. This refers to aspects like the length of your lines as well as the "genre" of the text: is it an abstract, an introduction, a comment, a description, a reference? Then make it so.
Even more clear or relevant may be the point of conciseness. We should try, as any good verse will, to be as brief as possible without omitting information relevant to the reader. That premise should be held dear, not only in reference to the actual text we create, but also concerning the information we want to display. Leaving out any kind of information that is not absolutely necessary is crucial for communication. This, however, should not neglect important issues of style (maxims such as politeness and coolness included).

2. Meter - Structure and Attention to Details

I will focus on meter primarily because of its attention to detail. Obviously, especially copywriters should be well acquainted with meter, since it is one of the ways to create a successful claim, slogan, tagline or catchy description. Research in cognitive studies and brain development has shown that, as infants, we learn the rhythms and meter structure of language first, even before having an understanding of what words may actually mean. This is a universalism, no matter which of the approximately 3.500 languages you learn as your mother tongue. Meter therefore is, and this is my point, the aspect of language most deeply rooted in the brain, which is why we need to make use of it.
The English language is, for the most part, structured in iambo-trochaic meter, meaning that most phrases follow varieties of this syllable pattern: unstressed-stressed, or stressed-unstressed, respectively. No great matter, but what I in turn would like to stress is that you need to pay attention to the details, which is why it isn't so easy to write good copy and why it usually takes a while to get everything just right. A slogan like "Watch it, hear it, know about it." works better than "Look at this, listen to it, and you'll understand.", although they essentially say the same thing.

3. Metaphors

The way that metaphors work in our brain has only recently begun to be explored by neuroscientists. However, as with rhymes, they directly relate to the part in the brain that is concerned with the processing of emotion. This makes them ever more memorable and appealing. So when you're employing the metaphor of, say, seafaring for a business website, there is an infinite number of images to choose from: from sails to waves, from fishing to mission, from whales to gales, from navigation to harbor station. When you get a metaphor to work for itself, which would be the ideal case, the reader will not only think: "Of course, that's obvious. It could be my idea." It also gives readers a context in which they can embed abstract concepts. So you have something you want to say (A) but you express it via a different word or phrase (B), which however clearly refers back to (A). It seems like an unnecessary detour, but it actually works, paradoxically, because a shortcut is created. A good metaphor makes an explanation (not an interpretation) obsolete.

4. Pragmatics

Pragmatics are concerned with all that goes beyond that what is actually said. So: not the literal expression, but what you want to get across. Look at FedEx's slogan, for example: "When there is no tomorrow." What is said is that there might be a case in which the day following today is not going to exist. What it means is that if you have something urgent to ship to someone who cannot wait another day, you had better trustfully place the important freight in the hands of this company and they will get it there faster than anyone else. A lot of this works by the deduction of context. As a copywriter you have to walk that thin line between saying what you actually need to, but making it interesting at the same time.

5. Self-sameness

This concept, coined by Henri Bergson, basically says that a great part of language is self-referential. This can be seen in the way that we perceive rhymes, assonances, alliterations, analogous sentence structures. Somehow we seem to need this and other structures to make sense of the world which is why you should employ it in your copy.

An Example

For illustration purposes and because it works so well, I will pick just one well-known slogan to briefly show just a fraction of how much poetics is in it and how it wouldn't work without. This is going to show you that you probably know more about poetics than you think. You just need to access this knowledge.

"Have a break. Have a kitkat."

It's easy to spot the analogous structure here. The two sentences are perfect equals regarding their syntactic elements. The great thing about it that through the analogy, the "break" (i.e. a "pause") is transformed into the actual product in the second phrase. Not to mention that you actually break the chocolate bars. There's no rhyme in there, but the assonances are elaborate in their simplicity: the ae and e sounds are recurrent and the vowel sounds of "break" [aei] are torn apart, reversed, but reappear in "kitkat" creating another analogy. The meter is broken in the word "kitkat", but only by adding a final syllable, stressing the word, without destroying the rhythm. Finally, the imperative form which actually is a violation to the maxims of politeness (which says you shouldn't tell anyone frankly what to do) is associated with something positive: a time-out, recovery and relaxation, pleasure.

To stay within the product category, I also like the Reese's Cups' slogan.
"Two great tastes that taste great together." Go ahead and take it apart.

While it certainly doesn't make sense to go through a procedure of analysis for every sentence you dribble out, you should keep the aspects mentioned above in mind as you write. Know about them and – with practice, re-working, and extensive reading included – your writing but also your conceptional skills will improve. On a side note, I think it was the legendary D. Ogilvy who once said: "Delete the best thing you've written and you start to get good."

Further Reading:

Consider adding these books (or excerpts of them) for your reading list. I promise they'll be worth your while.

Eagleton, Terry. How to Read a Poem. Malden: Blackwell, 2008.
Holland, Norman. Literature and the Brain. Gainesville: PsyArt, 2009.
Jakobson, Roman. Selected Writings: Word & Language. 2nd vol. Berlin: de Gruyter, 1971. 8 vols.
Schrott, Raoul & Arthur Jacobs. Gehirn und Gedicht: wie wir unsere Wirklichkeiten konstruieren. München: Hanser, 2011.