I don't normally shoot with studio strobes. My normal lighting setup includes a number of speedlights, which I prefer over studio strobes primarily for their portability. I don't have to have a separate bag to check on the plane with just lighting gear. That gets expensive and impractical for a lot of the travel I do. Speedlights are easy, I throw them in my camera bag or backpack and put my lightstands and umbrellas in my check-in bag with my clothes. I have a number of camera bags and backpacks so I can choose the bag that best suites my needs for that trip.
I love Think Tank's products and my primary travel bag is a Think Tank Airport International roller bag. It is well built, holds almost my complete camera kit, and is small enough to meet most airlines' baggage limits.
If I know I'll be on a smaller commuter-type plane, though, I'll use a backpack. I prefer not to loose control of my camera and have it shoved into the hold with everyone's baggage. For this type of travel, I use Think Tank's Naked Shape Shifter. I have customized this bag for the lenses and extra speedlights I carry on a shoot and it fits into the overheads of even the small jets.
For vacation-type travel, I switch to LowePro products because their backpacks include storage for personal items. The trade-off is less space for camera equipment. Since I don't need multiple speedlights, radio triggers, and multiple lenses when I vacation, these bags suit my needs perfectly.