This tends to become somewhat of a heated topic. Just FYI...
As a parent, I think it is our responsibility to keep our kids as considerate of other passengers as possible. That means that even though I would NEVER do it at home - if I see/hear a tantrum coming on - I will use M&M's to avoid it if at all possible. This, too, means no DVD without headphones. I know, I know - the 'would they rather listen to crying' argument is a strong one. However, IMO what DVD's really do is give us, the parents, a break (in many, many cases - in some, especially special needs kids - this MIGHT be the ONLY recourse to avoid crying). And really, if they won't use headphones, then I don't think we GET a break. Then we need to bring out the books, the goldfish, the M&M's (slowly, one at a time to make them LAST awhile), the crayons, the silly faces, the stickers, the stuffed animals, the milk or juice, reading MORE stories...you get the picture - way more exhausting for us, but that's our job.
When my kids were that age - I did it this way - ONLY let them hear the volume if they had the headphones ON. So they could watch it with no volume (Baby Einstein videos, etc would still keep their attention even with no sound) OR they could put them on. We got the old fashioned kind and it worked OK. But I had a bag full of alternatives just in case...
Good luck.