I'm officially consulting and self-employed, but for now I'm pretty much doing similar jobs to what I used to do as a staff employee. So I don't have multiple clients at the same time, but work a full work week, in an office, on a project, for months at a time. Eventually I hope to work smaller pieces with multiple clients (at higher rates).
What I like:
1. I get paid to do a job, not to fill a seat. If I do it well then I get paid well (much more clear correlation than in a staff job).
2. I am not expected to be in love with the industry that I work in. In my old staff job, I always got vague criticisms in my reviews which I traced back to the fact that the job is not my life. I'm good at my job, I think it's fairly interesting, but not more interesting than my life outside of work.
3. More variety in my job due to new clients, locations, etc. Also, working in a smaller environment, you often get a chance to expand your skills. You can work on the edge of your current knowledge and learn from others as you go (depends on the type of consulting you do).
Advice on how to make it work:
Even though my job is not quite true consulting, I can pretty much assure you that networking will be key for you. I only need to find a client every 6 months (sometimes projects run even to 3-4 years), but if you do short assignments then you need quite a few clients. People tend to give work to people they know, trust or otherwise have a connection to. Pretty much all of my jobs (and all the best ones) have come via my network.
What you need to know:
You need to be able to negotiate. Nobody will look out for you when it comes to money. Your rates can be high or low and that will be either due to luck or skill. I recommend skill. Know what other people are charging. Don't be afraid to set reasonably high rates, but be prepared to defend them (and potentially drop them if you overestimate the market). Hopefully you start with some experience so you already know that you have something tangible to offer.
Understand the tax implications. If you don't have withholding anymore, then make sure you put your tax obligation aside as you go. Nothing worse than a massive tax bill of money that you've already spent. (happened to a friend of mine, was not pretty)
Good luck.