Okay, this probably should have been obvious, but just in case this saves someone else a few minutes, here's the story.
Trouble with McAfee had me looking for an alternate anti-virus. I'd been happy with ZoneAlarm's firewall/anti-spyware, so I installed the trial version of their suite which includes anti-virus.
Everything seemed fine except for checking mail at Dreamhost with Pop3: e-mail to/from Earthlink and Pair worked fine. If I switched the Dreamhost mail to IMAP, that appeared to work, too -- though it was a low traffic mbox and I didn't do extensive testing, but at least the "check mail" didn't hang. Mail client is Eudora in case that makes a difference.
Since the only problem was with Dreamhost, I put in a support ticket (which I've since canceled).
Trolled the ZoneAlarm site and in their "instant support" tool found a recommendation to turn on "MailSafe" and turn off "any other application that may also scan attachments." Since the only "other application" running was theirs and since the problem appeared during connection, not during any scanning of attachments, it took me awhile to believe that recommendation. But when I found the configuration options in the Advanced setting on their Anti-Virus and turned off e-mail scanning, it seemed to correct the problem.
I'm not sure what the connection differences are with Dreamhost and, say, Earthlink -- but for now, I guess I'm okay. If anyone does have suggestions, I've still got 10 days left on the ZoneAlarm trial and I'm open to other options.