In standard tuning, I tune my low E string so that the G at the third fret is in tune instead of the open E note. That's usually going to mean the open E is a few cents flat, but that's preferable to having all the other notes up the neck be a few cents sharp.

For open tunings, I ignore the electronic tuner and tune the bass string by ear. Tuning it rxactly to the note it's supposed to be per the tuner never sounds right.