I have two children Quinn age 15 and Halle age 7.  I've traveled with both of them since birth; usually without another adult along.  I've run the gammut on travel:

Many parents struggle to keep their children seated on airplanes.  I love watching children have fun but the aisles aren't safe for little guys surrounded by adults and beverage carts.  Not to mention turbulance that could knock something onto them.  My solution is to strap them in:

When my children were infants I always held them close to me in Snugglies and hip carriers like Sarah's Ride even on flights.  They loved being close to mom and because of being attached they didn't try to get out of the seat.      When they grew into toddlers I took an FAA travel harness, like the harness shown in this link:  http://kidsflysafe.com/?gclid=CLv-nJu46pECFSEaawodtk6-ew .  I didn't have enough arms to carry a carryon, purse, baby and car seat.  The harness was ideal for travel!

When your child is old enough to stay belted in on the plane but you need a carseat for your destination, there are several options:  Take your own seat and check it as baggage.  The airline has huge durable bags to keep the seat clean.  You can always rent a seat from a car rental company but that can be expensive.  Or you can buy a new carseat.  I've purchased car seats and strollers at my destination because it ended up costing less money than renting and less aggravation not having to carry it around.  If you are visiting family they can hold onto it for your next visit or you can donate it before heading back home.

When you're traveling with an infant make sure they suck (pacifier, bottle, etc.) during takeoff and especially landing when the pressure changes in their ears.  I know first hand what it feels like to have painful pressure build-up and it hurts!  Check with your doctor to find out what to do should they be prone to pressure build-up while on a flight.

For all age groups take snacks!  Take some for yourself too.  I like to pack foods that I may not normally have, so the kids have something interesting to ponder, as they eat.  Do fun things like cut sandwiches with cookie cutters or sneak healthy veggies into a muffin, . . . Take sippy cups until your child refuses to use it.  My 7 year old daughter who is wise beyond her years choses a sippy cup at times so she can have beverages in areas of the house other than the kitchen.  You can also save the children's cups you get at certain restaurants and use those.  It is no fun to spill on a flight.  I've done it.

For traveling with children I love the magnetic drawing boards but crayons and paper work just as well. Children love doing age-appropriate crafts on a plane; they have to sit to do either activity.

As any parent knows kids love new toys.  Save a few just for travel entertainment. . .A close friend stocks-up on toys at garage sales and pulls them out during long trips.

Another source of entertainment is a portable DVD player!  I priced the option of renting for a roundtrip flight or buying and buying cost less.  If more than one child wants to watch and hear the movie, get an adaptor for the ear phones.  Put aside a DVD for the trip!  The kids will be enamored and you can relax! 

Take a blanket!  Traveling from Oregon to Florida last year my family, with the exception of my daughter who took a princess blanket along, froze on the flight because there weren't enough blankets for all of the passengers.  In discount shops or department stores you can find very inexpensive throw blankets.  You can even use it to cushion the portable DVD player in your carryon.

Once kids are teens, with Ipods playing in their ears,  you'll barely know they're on the plane until food arrives.  Then it's a free for all.

I hope these tips make someone's life a little easier.  I'm still learning. . .