Dive trips are exciting, but can be a real chore when it comes time to pack for the flight. There's the advantage of having all your own equipment and not using questionable rentals versus the task of getting it all to your destination.
Dividing equipment between carry-on and checked luggage can ease the burden slightly. Then the problem becomes, "What equipment should I check?" Here are four considerations to help with this decision:
If you're not allowed to have it on a plane, then the decision has been made for you; so don't even bother with that dive knife. I've heard mixed results from carrying pony bottles, with most saying they are fine. Check with the TSA's (if flying from the US) set of ever-changing rules for up-to-date information.
How expensive is the particular item? Don't expect the airlines to reimburse you for broken goods, just ask this guy. If it's expensive, you may want to consider carrying it with you.
Likewise, if something is likely to be broken when tossed (even inside a case), it also may be better off with you. There is a variety of luggage specifically designed for protecting dive gear, so you may want to give that a try. Keep in mind, however, that security may go through your bag and not put all the pieces back in exactly the manner that guarantees their safety.
How easily can you go without something? More so than just breaking something, luggage can get lost. If a checked item doesn't show up until the end of the week, will it significantly affect your diving? For this reason, most people will forgo their own weights on trips.
If it won't fit in an overhead space, then the choice has been made for you; either check it or leave it at home.
If you still have no idea what to do, then here's a starting point:
Carry-on: regulator (if expensive, but aren't they all?), mask (if custom or prescription), camera equipment (unless you have awesome traveling cases).
Check: BCD, fins, snorkel, wetsuit, knife.
Use the above criteria to tweak these lists until you are satisfied.