With restrictions on bringing liquids through airport security, many people travel without a water bottle, and then don't want to pay high priced for bottled water in the airport. But it is important to have plenty of liquids on a flight so you won't become dehydrated, and you don't want to rely on flight attendants for scarce cups of water. You can bring an empty hard-sided water bottle through security and fill it at a drinking fountain, or ask a flight attendant to fill it on board. If you carry a 1 liter water bottle, you should be set.
You don't want to rely on airplane entertainment on a red eye. If you have your own MP3 player, such as an iPod, you can use the headphones to watch the airline's movie or television or a movie you have downloaded. When you are reading a book or magazine that you've brought, you may want to wear noise-canceling headphones, which reduce passenger and aircraft noise.
You will want to take your shoes off to get comfortable on a red eye, and if you haven't worn socks, you should bring a pair to keep your feet clean. And even if you are wearing socks, a second pair is a good idea, since if you get up to walk around, your socks will get dirty.