I’m looking for ideas for little vignettes or encounters that PCs on a ship might encounter. Preferably story/social in nature, though the odd combat encounter isn’t out of the question.

Someones stealing food. Sounds petty, but on a long voyage, it can be a BIG problem.

Stowaways! Always fun for backstory and resolution.

Natura; hazards. Fog/storms/reefs all create problems that can be resolved by a number of skill checks.

Gambling. Sailors have downtime without many things to occupy them. Gambling is a time honoured tradition that can lead to any number of scenarios.

Fire on ship. From a stupid spell to a cooking mishap to a candle falling in rough seas, a fire onboard ship is one of the most dangerous things to occur.

Finding an abandoned or distressed ship. Do you help? Do you attack and plunder?

PIRATES. Always fun for some boarding and swashbuckling.

The lure of the sirens call. An encounter with sirens can quickly turn deadly.

RELEASE THE KRAKEN.

Passing another random ship on its way Fram points A-B. Do you share news from far off ports, avoid, or attack? Encountering different ships from various nations at war with each other adds extra spice. Maybe they have refugees, maybe their privateers, maybe their slavers or war vessels. 

Coming across small islands/archipelagos inhabited by indigenous natives, a Witch/Hag, a Cyclops, or some other nasty. Maybe even an "abandoned" smugglers hideaway. 

Ghost ship. 

Natural fauna like whales or dolphin pods. 

Mermaids, because mermaids. 

"MAN OVERBOARD!!"

 Here's a list of 100 things which I've plucked things out of.

http://dndspeak.com/2017/12/100-sea-travel-events/

Raise the stakes. Young crewman, fourteen? Twelve? Stealing food. Not much, but punishable by lash or something else quite severe. That'll create conflict between captain and characters (presumably, I know I'd react).

Here are a few.

A pod of dolphins swims beside the ship for a couple of hours
A sea hag disguised as a particularly ugly aquatic elf climbs up onto the ship
A badly wounded lizardfolk that's being attacked by a hunter shark climbs up onto the ship and collapses onto the deck
A merfolk swims up to the ship and warns them to turn around and go back because the waters aren't safe
Three Sahuagin swimming with a hunter shark attack the ship. They try to knock people into the water for the shark to attack.
The ship slows down mysteriously. Investigation finds a giant octopus hitching a ride by hanging onto the bottom of the ship. If the PC's attack it will flee by swimming straight down instead of fighting.

1) Ship board cat obviously intentionally relieves herself in one of the PC's cups.  If they chase the cat, have the cat lead them to the storage area.  [INSERT magic-user NPC] asks them retrieving a special MacGuffin on an island that's off course from where ship is traveling.  NPC promises rich reward to party if they get it.  [Island Sidequest INSERT].  MacGuffin turns out to be a Everlasting Catnip plant.  

2) Have the ship blown off course. Stormy clouds and thick fog surround it.  After waking up one morning, all the crew disappear.  Rats appear and eat all the food.  The party can't get any sleep.  The ship drifts to an island, which the PCs must explore or die.  Illusion of Despicable returning Villain appears to taunt them.  Actually turns out to be vampire lord/revenant/glowing artifact that got trapped on island years ago, promising a way to get off the island, but they must work together.  Tension, misunderstanding, possible murder ensue.  

Here's a random encounter table I created for the last session I ran my group through. They were traveling on a keelboat from Waterdeep to Daggerford so they weren't too far off the coastline. Easy/Medium etc. is based on a party of 3 7th level characters, FYI.

@Song_of: I like those ideas. 

Also how about a mysterious fog bank engulfs the ship for a night and a day. On the second night they come upon an entire ship devoid of crew with only one supernaturally beautiful, pale, passenger who thanks them profusely for rescuing her. And she has one large 3’x3’x6’ piece of “cargo” and would they mind  bringing it onboard?

I'm getting some serious Bram Stoker vibes.  Her name isn't Mina, is it?    (<_<)

Quote from Song_of_Blues >>

I'm getting some serious Bram Stoker vibes.  Her name isn't Mina, is it?    (<_<)

 It might be

Lots of great ideas here. Looks like my session is sorted. Thanks everyone!