Yes, without hesitation. There are two rules, though:

1) It must be relevant to the story. I'm not going to hock some products just for the sake of hocking some products.
2) It must not be overdone. That is so important - I've been to a few films where product placement is so prevalent that it ends up distracting from the actual film as you count the brand names that fly past.

Nothing wrong with product placement as long as it fits within the context of the story.

I wouldn't want to see pepsi and internet related "product placement" in a medieval story.  As long as it's within the context of our world, our present time or future, then I see nothing wrong with product placement.

That's one hadn't considered.  Now that you've raised it . . . taken within the context of my question - as an element within the storyline - if the character was reading a Wonder Woman or Powergirl comic book, then that would be a case of "product placement".  By contrast, I'd have to say for the real-world reader, a fan-fic about Wonder Woman or Powergirl would probably qualify as in-general unsolicited advertising.

The motivation, context, and degree of use make the difference between acceptable and annoying product placement.

One key point about product placement, whether it is a fan-fic or a soft drink, is that product placement depends on familiarity.

However, relying on character/product familiarity is a two-edged sword.
 
The first edge:
A certain amount of familiarity with characters or products can make writing more succinct and reading more effortless. 
One does not have to explain as much about a given, familiar character or product or how a familiar object works.

That is one of the problems that I have with some "other world" stories.  In some of those the writer gets bogged-down in explaining what a frazzlestuck is and what it does and how it works in order to show how creative he/she is instead of just calling the thing a toaster.  Like AlexG, I try to use plausible-sounding products in an attempt at humor and as a tangibility link for the reader.

Does it matter which brand-named soda pop a character drinks in a scene?  Probably not.
Does it matter what kind of car he drives?  Possibly; because for many of us that bit of information lends insight into the character's personality and socio-economic status.  The reader imagines a much different character if they are told that the character owns/drives a 1985 Yugo GV versus a 2008 BMW Z4 Roadster. 
To quote Dr. Emmett Brown in "Back To The Future" -- "If you're gonna build a time machine into a car, why not do it with some style?".  Quick show of hands -- if it were not for the movie, how many here would know what a DeLorean is?

That question is my segue to --
 
The second edge:
The problem with the assumption of familiarity is that what many of us think is familiar is not universally familiar. 
I did not know why a character was eating something called "Vegamite" until I looked it up.  (I can imagine my Australian friends cringing at my just-demonstrated naïveté).
And, how about the generation gap when it comes to familiarity with characters -- How many of us are facile with the seemingly endless list of sound-alike/look-alike Anime'/Japanimation characters?  A quick count showed that there are about one-and-a-half bazillion fan-fics about such characters.  However, no matter how well they are written, I won't be able to slog through a single one without my eyes immediately glazing over.  Yet, most of the folks I know who are still in college can recite encyclopedic details about most of them.

Great topic, AlexG!

Tschuss!
Hunter