The answers you are going to get will depend on the dive destination, the type of diver (i.e TraceMalin the uber tech diver vs. the PADI dude going to Cancun) and the anciliary equipment that diver intends to use such as a camera, lights, etc. All of which may varry in bulk or weight depending on the diver (i.e. 35 mm custom camera housing with dome port v.s digital camera, pistole dive light vs. can light, etc.).
Therefore, a hard core DIR/Tech dive like Trace will give you an extended laundry list of stuff the average scuba diver does not own, use or even know what it is.
The average open circuit scuba diver going on vacation might have a regulator set, fins, mask and light weight wet suit. Most of that will fit in a Dive Caddy type scuba equipment carrying system and will all fit in the overhead
DiveCaddy - Home
I have no beef with either form of diver, because we all make choices as to what we use, and why we use it.
On my last trip I tried out bringing a 13 cu ft pony bottle so I could go through the SDI Solo Diver course. Since I checked it, there was no problem.
What I typically cary to a warm water destination is:
Carry on -
Dive Computer because it is very expensive
Digital camera in it's housing with strobe
Regulator set on the way over
Log book with C-cards
Valve from pony to save weight in checked bag
Checked bag -
Mask (mine and wife's)
Fins (mine and wife's)
3/2 wet suit
Harness
Wings (i.e. BCD)
Pony cylinder
Dive skin (mine and wife's for snorkeling)
Save-a-Dive/tool kit
Booties/hood/gloves
Lights with battries removed
Regulator set on way home because bag was over weight anyway and my Sherwood warm water regulators are cheap compaired to my Poseidon oxygen clean regulators.
My rule of thumb is "if it is realatively expensive, fragle or hard to replace" cary it on.