S.R.
We flew with our 15 month old a while back and did not buy an extra seat - it was me, my husband, and 3 year old, so we had 3 seats amongst us. We did fine without the extra seat, but if it's just you and baby, buying the extra seat would probably be a good option. On the other hand, if the flight is not full, you can almost always sweet-talk the ticket agent into blocking off the seat next to you and getting the extra seat for free, but it's of course never guaranteed. One thing I wanted to add was that many international flights have basinettes which can accomodate babies up to 22 lbs. They attach them to wall of the bulkhead row. Our daughter was too tall for it, but just around the weight limit and ended up sleeping quite soundly for about half of the flight with her little legs dangling over the side. Also, when you check in, do request the bulkhead aisle, as it will give you a lot of extra room, which is nice when you need to retreive toys, baby wants to stand up, etc. Good luck!