You should have a phone number if you cannot answer all the questions about your product or services in an FAQ or about us page.
Then again--there is no right answer to this question. You mentioned 37signals, they are doing something right. Their products are not cheap (but very well priced compared to the market) however they were one of the first and got a lot of visibility and carved a very particular niche out.
If your message is so much aligned with your target audience on your site that when they arrive the total experience entices them to stay then...
YOU DON'T NEED A PHONE NUMBER.
**Here's An Idea**
Everything is is subject to testing--you can setup a funnel in Google Analytics to test how aligned your message is with your audience. Setup a 3 step funnel in GA and try to drive visitors through the funnel to a sale without a phone number.
check out Avinash Kaushik's site www.kaushik.net for more information on setting up GA funnels and every other imaginable concept on quality metrics.
For me I have ring central as well, no complaints, can get a virtual desktop "soft phone" and field live calls from your PC forward calls to your cell or google voice number. It's affordable even to test a new business idea.
There is no right answer to this question until you test your audience and niche and particular message.