Some clients come to me having found me through my website - if *your* website developing company website ranks high in their search, is nice looking, easy to understand, etc..., then they already have an idea of your capabilities, and what you can do for them. This works better in rural areas with less competition, and localized searches, of course. Perhaps that should be my disclaimer - I am not in a big city environment, I deal with "small business", so my method may not work as well there, though I think it would still work fairly well - people are people, and small business revolves around them.
The larger percentage of new website clients have come to me through word of mouth from existing customers, some from the website side but even more from the 'tech support' business I do. Being someone's IT guy really puts your foot in the door of not only that business, but into those of the friends of that business. There is a definite lack of personable, available, quality tech people in the independent sector, and to most people not involved directly in some sort of computer technology business, websites and fixing systems/networking/etc... are pretty much all closely related variants of the same field. You and I and I'd expect most /. readers know different, but there it is, in my experience. And if you know your stuff, and are personable enough that your clients know they can ask and trust your answers, your existing clients are your sales force - and a powerful one at that.
Your last sentence was something I used to ask myself about 10+ years back; does my new buddy Joe Shadetree really need a website for his backyard radiator shop? There is no question about it any more, the answer is a resounding "Yes!". :) ***Every*** business needs a website these days - the 'net is the first place most people look to find out about a business, even in rural America. Not every business needs a $10K website, though, and certainly not "Joe's Hometown Radiators" - it would take him forever to recoup that kind of investment. I do well selling "mom-n-pop" businesses with small requirements a 4-5 page, modifiable brochure site in the $700-2K range, using a custom design built on a CMS, running on a LAMP stack via a reseller account. This allows me to keep their cost low enough that after that initial investment of $2-5/day for their website and first year of maintenance/hosting, their ongoing cost for the site is a bit less than $0.50/day (if I don't have to work on their site much). For the ones who want to, however, they can log on to their site and update content, add pages, etc etc..., and all I do is make sure there are regular backups and upgrades. In this price range they are getting me for about 1/2 of what I charge on an hourly basis for the time I will put in on their site, BUT - I get a new, happy client, and a relationship that will likely last years, and put more money in my pocket over time than if I had gone full price to begin with.