Every traveler has an opinion on RTW plane tickets and we are no exception (in an attempt at full disclosure, we have never purchased RTW plane tickets, nor do we plan to in the future). Before listening to us, do your own research and develop your own opinion. Talk to travel companies like STA and see what they have to offer. It essentially comes down to price. Is it cheaper to buy as you go, or buy all upfront at once? Note these important considerations when deciding what is best for you:
Your Level of Flexibility: This is really the most important factor when deciding between RTW tickets or buying as you go. RTW plane tickets require you to lock in most major destinations and time frames for your trip. The tickets can be changed, but in most cases every change requires you to pay a substantial fee. Only if you're confident of your itinerary and accepting of limited flexibility should you seriously consider a RTW plane ticket. We've seen other travelers who wish to change their flight dates incur penatlies and fees upwards of $200. In some parts of the world, purchasing a flight costs the same as this fee for changing a ticket. So in these situations, travelers would have been better to not fork over the thousands up front for the RTW ticket, but instead, pay as they go.
Your Route: RTW plane tickets are most cost effective when you visit more popular "gap year" destinations. These flights are designed to go to hubs such as Southeast Asia, Australia, South America, and Europe. If you plan to venture farther off the beaten path, consider buying as you go. Adding destinations such as Mali, Iran, or Mongolia will quickly throw the cost of a RTW plane ticket out of whack. In these cases, regional airlines are almost always the cheapest option. Furthermore, RTW tickets often force you to move in the same geographic direction. All of your tickets must place you further east than your current destination, for example. This can hinder your route, or force you to buy extra tickets if you want to go somewhere else along the way.
Your Timeframe: RTW plane tickets are often limited to one year (although this is not always the case). If you're lucky enough to travel longer than that, you will likely have to buy at least some tickets during the trip. Consider how long you plan to be gone, and where you plan to be after twelve months of travel.
Your Age: If you are young, don't forget to look into student discounts. While rare, there are still some available. Also, at the risk of offending the young, we have to throw this out there: if you're young and stepping out in the world for the first time, you likely have friends and family that will worry about you. They will want some reassurance that you have a safe itinerary and schedule, and that yes, you will come home eventually. RTW plane tickets can provide some peace of mind for your loved ones at home. This is a valid consideration in your decision process.
For more information, Chris at AmateurTraveler.com has put together this great guide to RTW plane tickets. It covers different airlines and the pros and cons of purchasing tickets.
Using points to book flights is also something to research. Also, many people suggest that you use airline points to book hotel rooms, as it can be more efficient.
See also: the best travel pillows for long flights.