Firstly, you mentioned your CV. That is an academic term and has specific meanings. But if what you are really asking about is a resume, then just make sure your resume reflects why you are the right person or company for the job. In other words, write your resume specifically to be that nice juicy worm with the hook inside.

If by freelancing you mean long-term projects then you can just put them in as normal employment during the period. They are not going to do an IRS audit on you.

As for your description of bouncing around from project to project during your typical day, any future employer is likely to think you will not give her project adequate attention.

Also, feel free to list yourself as a DBA... Say that for four years you have worked for AwesomeTech and have done ..what? List projects that might seem relevant to your prospective employer. Use your company name as an indicator that you are available for the next project.

Cheers

Give project details in your CV. Do not just put freelancing etc. Also write what have you exactly done for those projects. Or you can create your own website and put your resume there, like this - http://shirsendu.com/resumedas.pdf

Unlink the projects you have worked in and your employment history.

Make two sections in your résumé:

• Projects, This should include side projects and everything that you consider relevant evidences to prove your qualifications.
  List technical details, e.g. development tools and platforms you have used (and supposedly you're familiar with).
  Indicate your role and the most interesting activities you have participated in, regarding each project (expos, contests, whatever).
  It does not matter who's the project owner. You may simply skip the employer's company name, but be ready to provide with references when asked.

  My personal preference is to have this section just after the contact info, as it seems to be the most important to me.

• Career, where all employers and formal positions (employment history) is recorded. You probably have this already.

Further reading from Workspace.SE:

• How should I list the employer for contract work on my resume?
• Incorporating off-job technical qualifications on resume
• Handling a Gap in Your Résumé

In the context of listing company by company, and the dates worked for each company, I just put 'independent', itemizing my project work.

An example would look like this:

1. Independent - March 2010 – Present
   • Project Management and Consultation
   • Created proposals, specifications and schedules for numerous clients Windows Development
   • Developed an Outlook extensions in c++ that provided ...
2. Company X - July 2008 - March 2010
   • Developed Excel quantitative add-in used by stock traders

The pain train

I was in the same boat as you for a while; I had ample experience over a few years where I worked on open source projects and websites for small-scale clients.

The easiest way to actually have freelancing on your CV? Put it there as previous work, and have some of your clients be references. It's as simple as that. As for the question of "will employers see it as valuable?", well, just put it there. Give them examples they can look at.

Portfolios

You're a web developer, which makes it really really easy to show off your frontend skills. We're also at the point where pretty much any developer these days has a Bitbucket or Github account, so there's the backend stuff.

Stick the websites you've worked on in a portfolio, and specifically target potential clients or employers with this (you can probably cram the usual HR buzz words in there somewhere, too).

Be sure to link said portfolio gratuitously in your CV and covering letters, too (I put mine at the start and end of my CV, make it short and sweet, and let the client take a look for themselves if they're interested.)

Frameworks

This one is web development-specific, too.

If you intend to be working with a business on any kind of backend code as a programmer (not a designer), you should learn the methodology and way of thinking behind nearly every framework for web development: MVC. It's also known as separation of concerns, too.

If you understand MVC, you can grasp nearly any framework in about a day or two of playing around with it.

tl;dr

Long story short: just put it down as normal experience, and if you enjoy the work you do, do more of it (the only way to get better at programming is to do more programming, for example). Start small if you like, and build up notability and a strong reason to get a client or a job.