Sometimes when I send a CV or I send a spontaneous application for a job, they often reply back to me with the same question: Why don't you want a permanent position? but I feel that the best question is: Why should I hire a Freelancer? Well, I am a Web Application Developer and this kind of work has a concrete factual basis, so I understand that this maybe doesn't apply to all positions. In my opinion, the advantages for the Client are:

1. Variable cost: A Freelancer is a variable cost, because he charges for the work done. In contrast to a permanent employee who works at a fixed cost.
2. Experience: A Freelancer has the experience and knowledge in a wide variety of environments (other projects, teams, technologies on different companies).
3. Lower costs (and worries): you are saving:  taxes, perks, training, hardware, licenses, workspace, vacation time, sick time, ......
4. Personal attention: A Freelancer is a self-motivated and client-orientated professional who will provide a higher level of personal attention. Referrals are our life.
5. Short hiring time: Quicker and easier hiring time, because there are no hard long-term contractual conditions.
6. Easier contract ending: If you are not satisfied with his work you can end the relationship quickly.
7. Flexibility: Freelancers are more flexible - long term, short term, remote, in-house, temporary, or permanent commitment.
8. Project focused: centered on goals and schedules that you have previously established.

Maybe it depends on the personality of the professional, but I think that all the advantages for my clients are also advantages for the Freelancer:

1. Variable cost: I can be more productive only acting when my services are really required.
2. Experience: Increase my portfolio and I can learn other technologies, techniques, work methodologies, ... and work with really interesting professionals.
3. Lower costs: I can distribute my costs much better because I know exactly what are my training and hardware needs. And I have control over all my expenses like taxes, vacation ....
4. Personal attention: I can work hard specifically on the needs of each client. I am building my own career, this is my main motivation.
5. Short hiring time: no more long interviews with two or three meetings for each one.
6. Easy termination of contract: If a client wants to change the Freelancer or finish the project, then just make a call or send a mail, without any more complications and in a friendly way for both.
7. Flexibility: No more fixed schedule. I am online 24x7 and this is my business, so I will adapt happily to my client needs.
8. Project focused: Each project is an accomplishment for my business and portfolio, so each happy client is the best marketing advertisement and therefore I can guarantee that I will be focused.

I think these lists depends on the personality of the Freelancer, but due to my own personal experience in my own professional career, I think this is the most sane relationship between a Company and a Professional.