I managed to create and then fix my own PEBKAC issue today and I thought I'd share the resolution in case it helps someone else out there Google-ing/Bing-ing for the solution.
The problem is failed logins and in your SQL error log you'll see entries like this:
Login failed for user 'DOMAIN\user'. Reason: Token-based server access validation failed with an infrastructure error. Check for previous errors. [CLIENT: xxx.xxx.xxx.xxx]
Error: 18456, Severity: 14, State: 11.
You might see these sorts of errors when you've got domain problems or kerberos issues, but that's not the case here. You can eliminate those issues if others can log in or if the broken user/users work when you grant them sysadmin server role membership.
Since granting anyone sysadmin (even on a dev box) just isn't acceptable in my world I had to dig deeper. It turns out that the real problem was that at some point I had denied CONNECT SQL to the DOMAIN\Domain Users group. DOH!
Probably not a common thing to do but this problem would manifest itself if you had done the same thing on other groups. Maybe you have a group of accountants you don't want poking around in the db, or a group of nosy developers and you revoke CONNECT to their AD group. Then the exception arises and someone needs access but they just can't connect despite you granting them permission. Look for that deny setting and you'll be all set.