Once you have your idea for a game, you need to do everything possible to protect it. That starts with forming your studio as a corporate organization. There are multiple ways you can do this; pretty much all of them involve filing documents with your state government.
You want to do this in order to avoid liability. If your studio gets sued, mismanages money, etc. you do not want to be personally liable. Therefore, a sole proprietorship and a general partnership are not acceptable options for most developers. These forms of corporate bodies do not provide limited liability, meaning that if they sue the company, you are personally liable to cover the company's assets. One lawsuit, not necessarily even a GOOD one, can completely wipe you out and bankrupt you. You want to avoid this at ALL costs. Paying a fee of a few dozen or even a couple hundred bucks (state dependent) is trivial to going bankrupt. Next, we'll talk about the kinds of business you can register.
LLPs -- a Solution for Small Studios.
Small studios may want to consider forming a limited liability partnership. In most states, this is done by forming a general partnership (usually explicitly, through a partnership agreement), and then filing forms to register the partnership as an LLP.
LLPs have a number of benefits. First, they offer limited liability. This is a must, as previously stated. Second, they offer pass-through taxation. In other words, the partnership itself is not taxed. Tax passes through to the partners incomes directly. This means, that if the partnership earns money, it can pay it out to the partners as income, and that income is taxed on the partners' personal income taxes. Similarly, if it loses money, the partners can deduct that loss on their tax statements. This often equates to less taxes in the long run. Also, adding and removing partners is relatively simple, and it creates a barrier between the senior leadership (partners) and contract employees who may come and go.
LLCs -- an Attractive Option
LLCs, or limited liability companies, are a relatively new concept that are an attractive option for some studios. You may not want to have a partner; you may not be legally able to form a single-partner LLP in your state. But, you don't want to be doubly-taxed by forming a corporation.
Most states now allow for you to register an LLC directly through their Secretary of State, Dept. of Corporations, Dept. of Taxation and Assessment, or other similar body. An LLC is a company, with limited liability. It can have officers and directors like a corporation does, but it features pass-through taxation like an LLP. They can also be much easier to set up than a corporation. For most small studios, this will end up being a very good solution. However, you should check with an attorney in your jurisdiction to see whether there are special rules for LLCs in your state.
Corporations: the Big Boys
Corporations are the traditional form of getting limited liability in a company. A corporation is owned by its shareholders; however they don't have to necessarily control the operations. Often, corporate directors -- the board -- manage the corporation (from a strategic point of view) and corporate officers, such as a CEO, operate it on a day- to-day basis.
Corporations can be expensive to create and maintain. They also suffer from double taxation -- they have to pay corporate tax on their earnings separately from the personal taxes of the shareholders. This means they may not be the best solution for a small studio. Also, because corporations can sell shares of ownership (stock), they are subject to more regulation, though typically this will not affect a small company.
Now I've got my Company Registered, What Else Do I Need?
Well, for starters, you need some way to protect the integrity of your game's intellectual property. Basically, you want the IP assets to be owned by the corporation, so that your game cannot be held hostage by individual contributors. (note: in this section, if I say corporation, I mean whatever form of company you go with -- LLC, LLP, etc.)
There are two ways to do this. For every new employee, BEFORE they do any work on the game, they need to sign a IP assignment. This is a contract that automatically assigns IP rights in all work done to the corporation itself. In addition, you will also want to sign a work for hire agreement. This is an agreement that ensures that if for some reason that the IP assignment was not valid, then any work performed was done for the purposes of giving it to the corporation, and the corporation will still own the IP.
IP Protections -- Registrations
Next, once the corporation owns the IP in question, you will likely want to register that ownership for additional protections. This can range from inexpensive (copyright) to very expensive (patent). It's always a good idea to register your IP if you can, but some indie studios simply can't afford it. You should consult with an IP attorney familiar with the games industry to get more information on what IP is critical to register, and what isn't. But do this quickly! There can be important time constraints on registering your IP that can effect your legal rights and obligations.
You will want other documents as well to ensure your studio runs smoothly. If you are going to have more than a couple of employees, you should have an employee handbook that outlines the rules and requirements for working for the studio. This gives you some protections should you need to fire someone, and can be useful in lawsuits over work requirements.
You will probably want to have a non-disclosure agreement for your employees, and for anyone you show your game to. This will help protect your game from being undercut by a competitor looking to steal your concept. Depending on your jurisdiction, you might want to consider a non-compete agreement, to prevent employees from running off with your idea.
Other administrative documents can help as well. Hiring contracts, purchasing agreements, contracts for awarding bonus compensation, etc. You should contact an attorney for these things to have them on hand, even if you don't need them right now.
As you can see, there are a lot of pitfalls to rushing into creating a studio. Yes, it is possible to have the next Minecraft or Counter-Strike without doing any of this. But having these things will make you more attractive to publishers, give you more protections, and with a good attorney they can be done at a reasonable cost.
You'll want to make sure you go with an attorney who is specifically familiar with the games industry, as it has certain quirks that entertainment attorneys based in film or music may not be familiar with.
In closing, protect yourself FTW, GLHF, GG, and make great games for everyone to play!