I bought my kids the new Ipod Nano. It plays their music, they can look at all our past Disney trip photos, and we can download their favorite movies and shows on it!! They are small and easy to carry. My kids are 9 and 4 and my 4 yr. old knows how to work it already! I think the DVD players are so bulky and heavy. The price was the same too. Also no movies to have to lug around! DD's Ipod was $200 and DS's was $150(the price difference is because of how much they can hold, I believe the $200 one is 8 gig?) The one my DS has we fit a ton of music and photos and he has 2 full length movies, and a bunch of shows like Mickey's Clubhouse and still has room for more.
Another option would be the new PSP. DH has this and loves it. He had the old model and just got the new one. You can also load your music on it, play video games, and watch movies.(The screen is a lot bigger than the Ipod Nano.) They sell a large selection of movies and you can get the movies for a good price on Ebay. DH always takes this on the plane. You could hook up earphones to it too. I believe it is in the $200 price range.