First of all, in the US in the IT area, there are essentially two types of contracting.
The first, usually called W2, means that you're an employee of the contracting agency. They handle the billing and other overhead, pay payroll taxes and usually offer benefits (quality varies by company). They bill the client, usually about 50% or more higher than what you'll see. For example, they bill the client company $80/hr for your time and pay you $45/hr.
The second, usually called 1099, corp-to-corp or freelance, means that you typically work directly for a company on a contract basis. Occasionally, you'll go through an agency but most people working this way prefer to cut out the middleman when possible. You bill your hours, pay all the taxes and don't have any benefits. The good part is that if you bill the client $80/hr all that money is yours, at least until you have to pay taxes (quarterly). Most people I know who work this way have a spouse who has benefits through their job.
In general, you'll see about 20-30% more on an annual basis as a W2 contractor. As a 1099 contractor, you'll see about 50-75% more although most of this goes for taxes and often you'll end up making less than the comparable W2 position once Uncle Sam and your state get their cut.
Other downsides of working as a contractor you don't get paid vacation and you're typically treated as disposable goods by the client. You can become the fall guy for regular employees if things go bad, even if they aren't your fault. You're likely to work less than 50 40 hour weeks in a year so you make have unexpected dry spells between contracts/projects. Even as a W2 contractor, but especially as 1099, you accept more risk and usually harder work for a higher monetary reward.
Lastly, as a contractor of either type, you're most likely to find yourself working in a standard corporate environment rather than with a Microsoft/Facebook/Google type company. You'll probably be doing jobs like maintaining old apps, doing work that the client company's employees don't know how to do or being brought in as a last minute replacement/addition on a failing project.
One more type is the contract-to-perm position. In this situation, a company wants to hire you but they want to give you a trial run as a contractor first. Since it's easier and less expensive for them to drop a contractor than to fire an employee, many companies use this. Typically, this is like the W2 contractor with a set hire-by date.