I prefer to carry on fly rods and reels when I fly. I have flown on trips when I have taken multiple rods, and on those trips I carried one rod on the plane along with my reels and put the rest of my gear in this duffle bag from Cabelas. It is light, tough and inexpensive. I strap in onto a carry on sized rolling carry on size suitcase.

http://www.cabelas.com/product/Camping/Luggage-Travel/Gear-Duffel-Bags%7C/pc/104795280/c/104744880/sc/104356080/Cabelas-Ripcord-Duffels/1315823.uts?destination=%2Fcatalog%2Fbrowse%2Fgear-duffel-bags%2F_%2FN-1100755%2FNs-CATEGORY_SEQ_104356080%3FWTz_l%3DSBC%253BMMcat1047 96180%253Bcat104744880&WTz_l=SBC%3BMMcat104796180% 3Bcat104744880%3Bcat104356080