All diving gear but cylinders presents no problems when flying as long as it is in checked luggage, even knives. Cylinders have to be emptied and their valves removed. It's really not worth the effort, since you'll have to take them somewhere, get them inspected, and filled anyway, and you could just rent some full cylinders from the shop pretty easily. Also, you will probably have to pay for going over the weight limit on checked baggage, which will definitely cost more than any savings you might get from having your own cylinders.
Another thing to think of, depending on where you are going and whether your trip is dedicated to diving or not, is "Do I need to bring any of my own gear?" On dedicated dive trips I do bring everything, but I have changed my mind on trips where I will do a little diving. In 2001 I took a 2-week trip to Africa, mostly doing the Safari thing, but I was also going to Zanzibar, and wanted to try Indian Ocean diving. I lugged all my gear to Africa, thinking "Hey, it's Africa, what kind of facilities will they have?" I left my gear at a hotel in Arusha while I was on Safari, picked it up on my way to Zanzibar. When I got to One Ocean Diving Centre in Stone Town, I was amazed at what a good operation they had, and all equipment, including masks, was included in the incredibly cheap cost of diving. The next time I go on a trip like that, all I will bring is what is necessary for sanitation - my own mask and snorkel, a mouthpiece cover for the regulator, and a skin to wear under the rented wetsuit. Still, when I finally make it to Palau, I'll bring my whole rig.
I always have a tough time understanding why people buy their own cylinders, unless they have access to their own compressor and either their own boat or great shorediving. It seems like the pain of lugging them around and cost of getting them inspected and tested annually would far far outweigh the benefit of owning them.