There could be links to your site, reviews, visitors who remember the name. If this is the case, letting your domain expire could be a huge mistake. A better solution could be, renewing your domain, and registering a new desired domain. In that case, you can set a forwarding to your new address.
What kind of domains are desired? For most cases, a short and memorable .com. For some cases, like local presence, you might want to register the local extension.
The other way to go is the 'SEO' way, which is to get keyword-keyword.tld. This way might be favorable if you wish to get easier Search Engine traffic.
NO! Register BOTH versions, and redirect one to the other. Otherwise, if you are bluewidgets.com, a competitor or such can register blue-widgets.com and steal away taffic from those who type in the domain name with a hyphen. Domain names are less than $10 a year.
As for ranking, for SEO purposes hyphens tend to be best.
I had an idea of renewing my current url, and buying the dot com, then transfering all the data to the new domain. Renaming the site in appearence and text.
Then for anyone who visits the new domain it'll be normal, and for anyone who vists the old one, they will get redirected and it will soon register with them what's happened.
A good example of this is the well known profile site now known as '<snip>'
It was '<snip>', but they changed their name to pull in more traffic and used the old domain to redirect.
[edited by: engine at 1:32 am (utc) on June 23, 2005]
[edit reason] Specifics TOS [/edit]