This is one question I'm asked from time to time, and it's a great question. Is phoenixwebsitedesign.com the same as phoenix-website-design.com or phoenix_website_design.com? To figure this out, let's look at how search engines interpret these 3 URLs.
Dashes, underscores or nothing?
Simply put, according to Google, they look at dashes as a space between 2 or more words, whereas they view underscores as joining 2 or more words. So, for Google, phoenixwebsitedesign.com and phoenix_website_design.com are the same.
Bing is slightly different. They look at dashes and underscores exactly the same - a space between 2 words.
So, to get the same result from both search engines, you'd be better to use dashes, But does it matter? Aren't search engines getting smart enough nowadays to figure it out?
Why it matters- the ongoing debate
The SEO community has debated for years, and continues to do so, over this topic. In Google's case, their algorithm uses over 200 benchmarks to determine a page's relevancy to a search query. Of course, there are more inportant items in that mix, and less important items. Max Cutts tells us not to get too hung up on keywords in URLs, however, a nice, easy to remember URL will trump and ugly, hard to remember one as far as user experience goes. That's why we have URLs - 126.96.36.1998 (not my real IP address) is going to be a real pain to remember, but citruskiwi.com is much easier.
Should I change my domain name?
Probably not, especially if you've had it for a while - it will have already built up ranking (asuuming you've done at least some vague SEO). However, make sure that you minimize or eliminate "session URLs" wherever possible. They're the odd looking ones with "=", "?" and "ID" in them. If you're on an Apache server (quite likely) this is pretty simple to do depending on your website platform. In my case, if phoenixwebsitedesign.com (or some variation with underscores or dashes) is available, you can buy that in addition to your existing domain name and point it at your main domain name.
The bottom line is be sensible. Don't throw away good, mature domain names that have page rank already. Don't get too hung up on having domain names with keywords in them. It's only 1 item out of 200+....