Wow, this was crazy. I ran SFC/scannow, and it said there were no issues. I checked Windows\\Fonts and Verdana was there (all four files). The dates/times/sizes were correct. I went into Word and entered some text and set it to Verdana. When I formatted it as "Regular" it displayed as iItalic. Even the preview in the Control Panel Fonts applet displayed in italics.
I copied the Verdana files from a Windows 7 VM with no change in behavior. Finally, I deleted the Verdana font from this machine and then copied it again from the Windows 7 VM, and that finally fixed the issue.
This is a new machine (a month old). I can't imagine what on earth might have happened, but thanks, guys, for the help!