The New York Times answers a reader's question about his email client, which can receive mail but won't send it from his email client. As the paper suggests, it's sometimes a tiny little tweak in your SMTP settings that saves the day.
Many companies, internet providers and email services provide two server addresses to their users to fill out — an IMAP address, like imap.awesomeco.com for incoming mail to be delivered to the user, and an SMTP address (smtp.awesomeco.com) for managing mail sending requests and other delivery features.
As the Times suggests, most email providers should provide detailed instructions on how to set up a typical email client, or even Gmail's account importing, with their services. Sometimes, though, companies make a switch to a different kind of security, or move a port number, and some customers are left in the lurch, so it's worth checking with the provider if a full double-check of your settings doesn't work.
If you're trying to set up Gmail on a desktop mail client, for instance, Google provides detailed setup instructions for almost any client, including Outlook, Apple Mail and Thunderbird. If you're using your ISP's email service (verizon.net, comcast.net, rr.com, etc), try doing a Google search for your ISP name and "IMAP", and you'll likely find some forum posts related to your exact same problem.
Q.&A.: When Mail Comes In, but Won't Go Out [Gadgetwise Blog/NYTimes.com]