So Equestria Daily has a story up about an online retailer that sells user-designed merchandise removing, apparently at Hasbro's request, merchandise tagged "brony." The response in comments, at least at time of writing Friday evening, is typically panicky and ill-informed.
Let me explain some basic copyright law. It will be basic, because I Am Not a Lawyer and basic is all I know; on the other hand I was the primary person responsible for keeping a $300K/yr content-generating business out of IP-related trouble for four years, so I'm not talking out of my ass, either.
Here's the basics: Hasbro (probably to some extent shared with DHX (the production study) and maybe Discovery Communications (who co-own The Hub)) owns the trademark on My Little Pony: Friendship Is Magic. They also own the copyright.
If you slap official MLP logos all over your stuff, you're in trademark trouble. I'm not concerned with that at the moment--it's obvious enough that most people get it. You don't get to pretend to be official merch if you're not, and using official logos and such is legally considered to be such a pretense.
People get a bit less clear when it comes to copyright, mostly because fans really, really, really want to be able to basically make derivative works whenever and however they want, including selling them, and really don't want to believe that they can't.
Here's the thing: If you are making derivative works of ANY kind, unless you fall into a fairly narrow band of works protected under the principle of Fair Use, Hasbro has the legal right to make you stop. As a general rule, for most stuff, they won't, because they don't care--your AU crossover fanfiction where Trixie is the Element of Mustard and has a torrid love affair with Deadpool doesn't do Hasbro any harm, so why waste time (which is money), people (who are money), and money (which is also money) going after you?
On the other hand, Hasbro makes money off of shirts, and every shirt you buy from a fan rather than an officially licensed short is money not going to Hasbro. Hasbro doesn't like it when money goes to people other than Hasbro, so yeah, they're going to exercise their right to get rid of those shirts. This is not Hasbro asserting ownership of the word "brony," it's Hasbro noticing that any shirt tagged "brony" is almost certain to be a violation of their copyrights, and therefore asking a shirt-design company to start removing the shirts tagged that way.
Not only is this completely within Hasbro's rights, this is what copyright is for. The exact same principle that gives Hasbro the right to stop you from selling MLP t-shirts (or, for that matter, if they want to, posting MLP fanart to the Internet) is the principle that prevents 20th Century Fox from turning my bestselling novel (I haven't written it yet, but give me time) into a movie without my permission and without paying me any money.
So, bronies of the world, do please sit down, shut up, and try to understand that just because you enjoy doing something and have gotten away with it in the past does not actually mean that you have a right to keep doing it.
(And no, what I do is not the same thing. There is an explicit Fair Use exemption for works of a scholarly or educational nature, as well as reviews, and it is one of the exemptions which is allowed to be for-profit. Hasbro has the right to make me pull down my fanfic, but not to make me stop selling my books.)