If you are traveling anywhere you'll need something to keep your clothes and gear in. It's not good enough to stuff it all in your board bag, as much as you'd like to. If you are only going from your house to the local beach then any board bag will do, but not for a serious trip.
If it's a short trip, you are probably after one of the smaller items like a duffle bag or a carry on, if you pack light. For a longer trip, you'll need much more space. A split luggage is useful as it lets you separate your surf gear from the rest of your clothing clothing and accessories. No point waxing up your going out outfit!
Roller bags are a great idea, if you have a 100+ltr bag and have a surfboard bag or two, they can really help take the load off.