I myself have had a number of interest via the website. Its a place of checking out who you are - so always include information about your company, your back ground etc..
Nowadays people want to know who they are getting for their services.
You can also advertise more of your services via the website than you ever could advertising via YP for example. Plenty of pictures of before and after your services always go down a treat.
People can pay you online via your website too.
Most companies have a website nowadays and its easy to jump on the net and search for someone - i do it all the time, rather than flick through the yellow pages, if i could ever find it.
The better the website (not only design, but also information), obviously they have paid money on it, so are more likely are going to be a reputable company which is not going to disappear.
Its not only the young that do it, its also the professional types that dont have time in the evening, and do it at lunch at work or the older generation (like my mum) she uses the internet more than i do!
I wont pay for advertising online anymore like Yell.com, as my website can be found easily via a window cleaning search via google, which is how most get to see my webpage. The rest come by it via one of my flyers.