Typhoons, Hurricanes, illnesses transmitted onboard. AC breakdowns, freshwater rations. Local Dock unrest or labor strikes, Piracy.
In 20 years at deep sea, mostly on liner container vessels as officer in all ranks and master, I rarely experienced any of these.
I met a hurricane once, 200 miles of the coast of New York. That was bad.
There are weather services, and weather routing, and masters and companies do everything possible to avoid meeting a tropical storm. Sometimes can not be avoided. But you can choose a season to take the trip out of the tropical storm season. But chances in any case are small.
Illnesses, never - had only few kidney stones, and one STD collected in port by crew member, with emergency disembarkation, (scorbut epidemic does not happen any more, for last few centuries, and crew has valid medical fitness checks, one year validity).
Freshwater rations shortages, do not happen - water maker in use, 20 to 50 tons production per day, depending of the size of ship, and fresh water tanks are chlorinated and yearly certified for domestic use - thus drinkable, and every 3-4 or 15 days the ship is in port where it takes supplies including bottled water.
AC breakdowns.
AC is only recenty added in ILO convention as mandatory. Not so long ago, many ships did not have that at all(you can suvive withou ac). My first ship did not have AC and did not have GPS.
But, now is mandatory, My experience, loss of AC, in the worst case is one or two days, till they fix. There is ch electornic, chief electrician, Ac technician. And this happened maybe a few times, and I am on the ships or offshore since 1995.
Keep in mind that there are hundreds of refrigerated containers in transit, and the company will have trained, experienced personnel to fix a reefer container or AC problems on board.
Dock unrest and labor strikes, I have never seen it or affected the ships.
What I can assume, company will know about the strike, and the ship will be diverted to another port.
The worst thing that can happen is an additional day or two at anchorage. You can spend fishing at the stern, or the master can organize barbecue during that time.
Piracy remains an issue:
Somali coast
Mallaca and Singapore Strait
West Africa, Nigeria and neighborhoods
First, choose your trip wisely, avoid these areas.
If you must go there, you choose your ship wisely. If you find a route, ask the company name of ship and ships speed (technical details of the vessel can also be found on the internet).
Pirates never boarded the ship with speed over 15 knots.
Ships boarded up to 12 knots
Shots fired at vessel at speeds 15-18 knots. Small arms fire
20 knots, they do not even try.
Fast container liner runs at 20 to 24 knots.
Do not board VLCC tanker, or bulk carrier (Vsl speeds are less then 15 kots) in piracy areas if you dont have to.
I had piracy attack (attempted) once, we turned search lights on the approaching skiff, and started fire pumps with hoses directed at them, plus sounded a very loud alarm. Mallaca - singapore strait, eastern approaches. Actually it was me at the watch, started all actions, and then called master.
Pirates turned and never tried boarding. 26 years ago, around year 1999.
99.9% cargo ship travel is safe.
We had more problems with passengers.
Ship rolls at high swell, an elderly lady slips, and breaks a leg. Now organize medevac. Mid Pacific.
Passengers forgot their blood pressure pills, forgetting diabetes medicines, and discovered that at about half of the Atlantic), or disembarking and forgetting part of their luggage (on the opposite side of the world from where they live).
Ships, BTW, have a hospital with basic medicine supply and can improvise with basic medicines in such cases. Next port, required medicines will be organized and delivered by agent.