This is a tricky one. Coming from the Design industry, mainly web integrated work - I will try to give two sides of advice.
First let me start by sytaing that the "mystery" is really gone from web design. And anyone here on this post that is practicing web design can vouch for the fact that deep down inside when you build a site for a client you know that what you are building may be historic in only a matter of months. Or maybe I am speaking for myself when I say that, BUT think about it... Web 2.0 has opened the doors for business leaders to really scale their web experinces and deliver data via the web in a more interactive format now, more than ever before. Am I saying that businessesdont need a website? Nope. BUT I am saying that the days of a "robust" solution is gone. As a former web designer I spend more time deprogramming my clients on these truths then building or designing new websites. Web Designers should be transitioning to more consultive/strategic positions vs selling websites... This is of course opinion BUT let's look at this...
Say XYZ Company needs a Website? Say XYZ Company really wants to communicate it's products and services to the world... How do we manage the content? CMS? How relevant is the data on the site? "About Us", "Contact Us"? What part does the site vistor play into the content and experience of the site? None perhaps? How personal is that..?
Websites are quickly transformimng into web applications, and there is literally no way for a business leader to compete without becoming involved with his/her web pressence. The old proposition was... Hire a design company, talk about the design and the content, set up the structure, drop in a few web forms for contact purposes, a bit of SEO, and 6 months later "Extinct". The new proposition looks a bit like this... Talk about brand and message, organize content and discover niche data, layout the web applications map (what your using, MySpace, YouTube, Jaiku...blah blah blah), set up content delivery schedules and feedback schedules (1 time a day? 2 times?) - I could go on... BUT I think we see the shift in thinking... Websites = Extinct. Web Activty = Distinct & Relevant (not to mention fresh).
Now, am I saying do not get a Website? Nah - not at all... BUT I am saying you can reduce your cash outlay for a site by building the straight forward who, what, where, why deal, with ties to your online activity...
So my answer to teh original question... Who do you recommend to design a website? LOL!! Definitely not a web design company! Not anymore, UNLESS they have shifted their mindset to a Web 2.0 (web friendly) mindset. My clients look for coaching, not so much building, they are looking for information organizers more than anything... Application Consultants, YouTube content developers, and optimizers, MySpace Designers, Mind Mappers...
Welcome to the future...