The answer is that it depends.

I know this can be a frustrating answer, so let me elaborate a little bit. There is a  wide range of situations in which a hashtag comes to be associated with your brand, so let’s break it down a little bit. There’s no yes or no answer. 

The important thing is this: exactly why are you thinking about protecting your hashtags? What is the main motivation? 

If your answer is that you will be able to stop other people from using it on Twitter or on Facebook, then it won't work. The use of any hashtag cannot be regulated by trademark laws. I can use any brand name as a hashtag in my posts or mention them in a book describing that brand. 

When I say I love to eat at McDonald's, McDonald's legal teams cannot follow up by suing me for using their trademark. Even if I say I don't like to eat at McDonald's, they still won't be able to sue me for using their trademark. It's simply not a trademark infringement. Even if you trademark a hashtag, you will never be able to stop people from saying good or bad things about your brand.

Keep this in mind. In certain cases, it actually does make sense to trademark your hashtag. Sometimes, a hashtag is how people know about you, and might even be what they think about when they are thinking of you. If a hashtag is how they found out about you, that may be how the consumer has labeled you in their minds. 

When your trademark is a hashtag, people will use that hashtag to locate you. If your brand name is unique, you may get lucky, and not many other posts will be under that tag. Even if it is a highly used tag, that means everyone who is searching it has a chance of seeing your posts.

If you've developed a hashtag that everybody already associates you with, then that would be a good idea to trademark. But again, don't trademark it simply because you think that you'll be able to write a letter to Twitter with complaints of the hashtags’ use across the site. That's not gonna work–I promise!