Will Harry Potter ever enter the public domain?
Objectively the answer to "will it enter public domain" is yes. According to The Duration of Copyright and Rights in Performances Regulations Act (1995), the Harry Potter books will enter the public domain 70 years after the death of the author, J.K. Rowling.
5.12.2 : Copyright expires at the end of the period of 70 years from the end of the calendar year in which the author dies...
Assuming she lives to be 81 years of age; the average life-expectancy for a British woman living in Scotland, we would expect to see the books leave copyright (in the UK) around 2118 A.D.
When you extrapolate trends in copyright legislation, then Harry Potter won't ever enter the public domain, because it's not older than Mickey Mouse.
For several decades the Walt Disney Corporation is investing a lot of lobbying resources into extending copyright protection durations. The reason they are doing this is because they don't want their classic cartoon characters like Mickey Mouse or Donald Duck to ever fall into the public domain. They have successfully done this in 1976 and 1998. And as long as the company exists and still has the economical and cultural significance it had for the past decades, it will keep lobbying for further copyright duration extensions. Should Disney lose influence, other media companies will likely make up for it by increasing their lobbying efforts in order to protect their intellectual property from the past 100 years.
So unless all currently influential media companies die and get replaced by new companies whose main intellectual properties are all younger than Harry Potter or we see a major change in the way politicians make decisions about copyright legislations, we can not expect HP or any other currently popular IPs to ever become public domain.
The duration of copyright governed by the country of origin. This is the country in which it was first published (for books) or released (for films) or, if published/released simultaneously in multiple countries, the country with the shortest copyright term. Simultaneously here means "within 30 days".
To further complicate this, not all countries observe the rule of the shorter term, including the United States. This means that a work may be public domain in some countries but still under copyright in others.
For the first book, Harry Potter and the Philosopher's Stone's country of origin is the UK (published 26 June 1997) so the UK duration applies. This is 70 years after the calendar year of J.K. Rowling's death (which has not yet happened, of course).
Later books in the series were published simultaneously in many countries so the exercise has to be done to see which one of those gives the shortest term - I'm not going to do this.
The same applies to the films. Harry Potter and the Philosopher's Stone was "simultaneously" released in 34 counties (UK, USA, Canada, Ireland, Malta, Taiwan, Belgium, Philippines, Switzerland, Germany, Malaysia, Netherlands, Singapore, Austria, Brazil, Denmark, Finland, Mexico, Norway, Sweden, South Africa, Argentina, Australia, Chile, Israel, New Zealand, Colombia, Spain, Greece, Guatemala, Iceland, Portugal, Uruguay, Japan) - work out which of them has the shortest copyright term and you have your country of origin.
Because films have joint authors, the copyright term is measured from the last of the authors to die. You also need to determine who the "author(s)" of a film are. UK law defines the authors as all of the principal director, author of screenplay, author of dialogue, or composer of music specifically created for and used in the film (you will note that each of these could be multiple people). The US law doesn't define it - is it everyone who appears in the credits? If so, the UK duration will be shorter (or at least not longer) than the US duration.
Notwithstanding the expiration of copyright, if elements of the property are still being used commercially (e.g. "Harry Potter", "Hogwarts", "Ministry of Magic", house logos etc.) they are protected by trademark law.
Other answers have covered the current copyright situation.
It's important not to assume this will apply in future though. The Sonny Bono Act was explicitly enacted to prevent Disney's copyrights from expiring. Since they have successfully done this once, it would be naive in the extreme to think they would not do the same again in future. It's a simple cost-benefit exercise - will the money from future income on copyrighted products exceed the cost of the bribes (ahem, "campaign contributions") to enough law-makers to swing the vote? If so, bring on the bribery (ahem, "political action committees").
Yay, free markets - so long as we are the only people allowed to set up stalls there...