Very dependant of where you dive and the type of diving you do.
For this reason it's not necessarily valuable to compile an "overall most common emergency" list. This is why we teach divers to make an assessment of the dive environment, the dive plan, the dive gear, and the divers BEFORE any dive. After doing that it's very simple to determine what sorts of issues might occur on a given dive, and then:
A.) Modify (or abort) dive plan to obviate certain potential issues
B.) Be on the lookout for other potential issues during the dive in order to avert their occurrence
C.) Have appropriate gear and contingency plans to handle such incidents should the occur anyway
Think about it this way:
Yes, OOA can potentially occur on ANY dive. However, if the dive plan is for 30min on a site with a 35ft max depth along a basic coral reef with no overhead, few/no entanglement possibilities, no current, and a simple shore entry/exit with 85F water... with an appropriate dive plan, gear, and training the likelihood of going OOA is low, the diligence needed to guard against it happening is minimal, and the contingency plan to implement if it DOES happen is very simple. You probably don't need to dive doubles, bring three lights, have four cutting tools, etc, etc.
On the otherhand, if the dive plan was to 100ft on a busted-up wreck in an active fishing area with 10ft of vis and a bit of current you'd want to consider and plan for things like:
- depth vis-a-vis gas planning and narcosis
- entanglement hazards based on likelihood of monofiliment, nets, traps being present
- potential to encounter partial/full overhead situations
- likelihood of buddy separation
- potential to become lost/disoriented
While there are five things (and more) on that list, they can be minimized/eliminated/managed by things like:
- ensure the dive plan is within your training and experience
- run gas planning calculations during dive planning
- plan to stay on top of wreck at 75ft to reduce consumption and potential for narcosis
- bring redundant air supply
- ensure all gear is well-maintained and in good working order
- be on the lookout to avoid entanglement hazards, and bring appropriate cutting tools just in case
- clarify among team that there will be no penetration
- plan to stay within sight of buddy at all times
- bring a reel and/or other navigation aids (strobe, compass) to ensure you can return to upline
- have an SMB to deploy from depth or at surface if you get lost/separated
- have a whistle and other signalling device in case you surface away from the boat
- ultimately remember that ANY diver can call ANY dive at ANY time; if risks are too many/significant... they can ALWAYS be completely eliminated by not doing the dive
When you think about it that way... the number of realistically anticipated emergencies on any dive is ordinarily fairly limited, readily identified/predicted, often easy to avoid, and usually straightforward to handle if they should occur despite planning and diligence.
With proper planning, training, equipment, and dive execution there should be few if any "emergency situations." Rather there should really only be "minor nuisances."
Ray