General tips for flying alone with small children

Whenever possible, buy non-stop tickets. Every transfer adds peril. And don't be fooled by the phrase "direct flight" — it only means a route on which you don't change planes, NOT a non-stop.
Never go first class. Never. First class is full of over-tired business people with $4,000 laptops and non-plastic glasses with red wine in them. Enough said?
Try to buy tickets for the least popular times and routes:
Saturday is usually a light travel day.
The last flight before a red-eye tends to fill up.
Try to go on new routes for established airlines — it takes a while for travel agents and businessmen to discover these routes.
If you buy a seat for your child, ask for the aisle and window seat on planes that have three-seat rows. This will leave an empty seat between you; if you and the child have the same last name, most of the time ticket agents will keep that middle seat open for you as long as possible. On the rare occasion a businessman is inadvertently placed between you, he will generally be more than happy to move to another row, leaving you with that most precious of commodities — an extra seat.
Fly so that your child's normal naptime coincides with the middle of the flight. Try to avoid flights where naptimes overlap with boarding or de-planing — times which are too full of stimulation, tension and harsh intercom voices.
Consider, also, time changes and jet lag. Try to arrive at the destination an hour or two before bedtime in the new time zone. This gives everyone time to visit, eat and decompress, so that the over-tired child can then fall into bed and begin sleeping — that very first night — according to the new time zone. Another strategy (particularly good when going westbound) is to arrive a couple of hours past their usual bedtime. Again, this helps increase the chances that they will go to sleep and stay asleep until the new time zone's usual awakening hour.
Be upfront with your fellow seatmates. I used to hold my wiggly pre-toddler above the surrounding rows as we boarded, and say loudly, "Your worst nightmare has just come true: a toddler is sitting near you." Right away, I learned what kind of seatmates I had: people who loved kids, people who wished there were child-free airlines, people who were clearly going to be a lot of help. Nowadays I lean over the row in front of us and say, "My 4-year old is sitting right behind you. He's an active boy but we try to be very well behaved on planes. Please let me know if he does anything that bothers you." Again, everybody's on notice that you are a responsible parent in a difficult situation, and you find out, right away, who your friends are. Because you definitely need friends on long airplane flights. If there ever was a place where "It takes a village to mold a child," it's at 36,000 feet!