We took my son to New Zealand when he was 3 3/4. I was really dreading the 24 hour flight but I figured it couldn't actually be worse than childbirth & I survived that!
But actually it was completely fine.
We went Air New Zealand straight through, with an hour or so's stop in Hong Kong (which has a small child's running around facility plus showers). My son does like planes, eating and TV which really helped. The seats on the plane were bigger than average and they had a little packs for all the kids. The kids' food wasn't much good - he much preferred eating mine.
We brought a small case with toys, sticker books, DVD player, cars, colouring pens, snakes and ladders, ipod with audio books etc. We went for little walks around the plane and made some friends.
We only had one minor melt-down, after which he promptly fell asleep for the next 9 hours.
I would take PJ's and a pillow so they know when it's bedtime. I also forgot a change of clothes - not o great when he slops noodles down his front in Terminal 3 before we even left!
He really really enjoyed New Zealand. And it is a memory that will last forever.