Yes, but not as much as it used to.
A good domain helps your search ranking. For example, a domain specifically related to your market might help you show up on page 1 of a broad Google search for something you offer. Whereas an obscure domain name is less likely to trigger those kinds of broad search matches.
A good domain might be easier to remember. For example, if your domain is longer, or uses abbreviations or variations on your company name rather than a simple Amazon.com-esqu domain, people may have trouble remembering it. That will cost you more in marketing than a better domain name would.
However, the availability of new domain extensions beyond the traditional .com or .net’s, the new and developing algorithms for how search engines rank websites, and the prominence of social media and other newer marketing channels, your domain name has become less of a defining factor in your success.
The keys are:
- It should make sense
- It should be catchy (easy to remember)
- Spelled the way it sounds (preferably)