Depends on what you mean... Have I headed out without a map? Sure, on little day hikes around Seattle.
Have I ended up without a map in the middle of the Alaska wilderness, for one reason or another? There have been times...
Probably the longest I've been off-map was about 4 and a half days, heading down the Alaska Peninsula with only very rough and inaccurate sketch of the coastline we'd copied off a wall map of the state. This turned out to have the key rivers in the wrong places (probably our poor copying). After the 4 and a half days, we ended up at the Aniakchak cabin, and got to look at the map on the wall there. It was another day or so before we were back on our map.
This is why I no longer order maps and have them mailed to me in the middle of nowhere before I see how they line up...
I've been off-map for a couple days coming into Seldovia at the end of the Kenai Fjords trip. That wasn't really a problem, since we (especially Hig) knew the area well.
Otherwise, I think all my off map excursions (usually due to me not being generous enough with how much extra map I printed out) have been less than a day. This summer, I walked off my map for most of a day, trying to go inland enough to avoid the swamps and sloughs along the Kvichak River. And I've done it for several miles here and there occasionally (I'm remembering one time in the Brooks Range).
Though most of these off-map excursions weren't planned, I don't think it's necessarily a bad idea. Hig and I have toyed with the idea of going trekking somewhere we've never looked at the maps for (maybe somewhere like the Ogilvie mountains?) just for fun. It would be a very different style of trip, of course. But people used to do it all the time.
All my wanderings off the map have also been off trail. And I think that's actually safer. It's much easier to get problematically lost on a trail, since you're hanging your hopes on the trail to get you somewhere, and don't have to pay as much attention to your surroundings. And if the trail isn't going the right way, its harder to correct your course. The three times I can think of that I've gotten temporarily lost have been on trails (two animal, one human).