This seems to be a very common concern among all striving entrepreneurs, especially in the board game development field. Some developers are incredibly worried that someone is going to rip off their idea and create their game before they have a chance to do it themselves. It's a very human feeling, especially with all the media sensationalism surrouding some high-profile cases of intellectual property theft, such as the Facebook or "Ice Ice Baby" controversies.
I don't know if it will come as a relief or more fuel for anxiety to know that board games cannot be copyrighted. Yes, that means that anything you create can be "copied" by someone else... but it also means you don't need to worry about copyright fees or lawyers. Personally, I'm glad that it's sort of an open market for game mechanics. More on this later. First, you need to understand why it doesn't matter anyway.
Say I'm at a convention and have been drinking. I tend to roam around and talk to interesting looking people when I drink. One thing that consistently grabs my attention is a prototype. If I see a table full of people gathered around something that looks like a Crayola advertisement that is literally held together with Scotch tape, I'm immediately interested. I want to know what this cool new game is about. Is it a war game? A worker placement? Is there dice rolling? Player powers? I want to know more, and there is usually someone at the table that can give me the information I desire (generally the developer himself).
Nothing will shut down an interested audience faster than refusing to talk about your product. Aside from the subtle implication that I'm a thief, I'm disappointed. Good luck selling me your game later if I don't even know it's yours, or if I leave with a bad taste in my mouth from the interaction. Besides, no one is going to hear about your unique mechanic or theme and say to themselves, "Oh boy, I can use this."
Seriously, no one.
Your idea is the greatest thing in the world... to you. I have so many ideas in my head that I don't even know where to begin. I've had ideas for everything from board games to radio modifications to a specialized fork for eating salad. Before I'd even begin to entertain the thought of stealing your idea, I'm going to begin (or finish) execution of my own ideas (which, by the way, are the greatest things in the world).
The old cliche is true: ideas are cheap, and execution is everything. Even if I decide to steal your idea for a game involving a battalion of squirrels invading an oak tree inhabited by a mean bird, you can do it better. You have all the details and the nuances planned out in your head. You know what the art is going to look like. This is your game, and your heart is in it. Mine would be a cheap imitation, even if the original is not yet produced. Besides, how many games are rehashes of naval trading off the coasts of Europe? Theme ideas are cheap and everywhere.
Mechanics are similar. Mechanics should fit your game like a cog in a well oiled machine (pun partially intended), which doesn't lend itself well to being stolen and shoehorned into a different game. If you have mechanics that can be drag and dropped into any other game, then you're already severely lacking in the originality department.
So we've discussed that themes and mechanics cannot be legally protected, but is there anything you can do to defend your work? Well, you actually don't need to do anything at all. All your work is copyrighted simply by existing. That doesn't really help much anyway since, as I mentioned, virtually nothing about a board game can even be protected.
If it helps you sleep at night, you can copyright your rulebook text, cards, and any original art/design as literature. For our fellow Americans, this can be done online for a small $35 fee, which is pretty reasonable. Do not bother with various "Poor Man's" methods or copyrighting, such as mailing yourself designs and leaving the envelopes sealed. They don't work. Like, ever. If they did, I'd have mailed myself a bunch of unsealed envelopes and "invented" all sorts of stuff.
You can also patent certain game mechanics, but my impression is that it's extremely hard to enforce and not really worth it. Basically, unless you're Wizards of the Coast and patenting Magic the Gathering on the whole, don't bother. Considering the fact that most board game ideas never even get produced on a large scale, much less become very profitable, it's very hard to justify the cost of patents anyway. If you really want to patent something, talk to a lawyer and expect to pay between $5,000 and $15,000 or more.
Another thing you can do is register trademarks for any names, characters, or theme universes. If you intend to create a series of games within the same universe, a trademark may be worth looking into. Trademarks are also granted by simply existing. If completely ensuring the protection of the fictional names or characters in your game is important to you, you can also legally register trademarks. Here is the definition of a trademark and when to use one, according to the US government. Depending on the specifics, trademarks can run you from about $300 to over $700. If you wish to pursue a trademark, I'd highly recommend hiring a lawyer. On that note...
I have absolutely no legal training or background. Everything I typed can be freely found on the internet, so please do not take anything I said as legal advice. If you're considering any sort of legal action to protect your intellectual property, please speak with someone qualified to give you advice that pertains to your specific situation. You'll be doing yourself a favor.