You Know What People Want In Their Cruise Ships? Water.

*EDIT*
As pointed out in the comments section, the first ship to have an on-board swimming pool was not, in fact, the the RMS Olympic as stated below.  It did have a pool before the Titanic, but unfortunately for me, after having written this long post, it was an earlier ship in the White Star Line fleet that had the first on-ship pool.  The honour goes to the RMS Adriatic, not the Olympic.  And certainly not the Titanic.  I'm keeping the article because it's mainly about the frequent confusion between the Olympic and Titanic, with the pool being the focal point for that, but please, as you read, keep in mind that my initial research was wrong and it's not actually the Olympic that had the first ocean-going pool.
*end EDIT*

Let's say you're building a ship in the early 1900's.  Let's say you're building the largest ship known to man at that point.  Let's say that you want it not only big, but luxurious.  Let's say you do it.

So you've got the world's largest ocean liner, and you need to think of a way to make it more luxurious.  You may not be building the fastest ship on the seas, but damnit, if people are going to trapped on your ship, they're going to enjoy it.  So what do you add that no other ship has?  You got it, a pool.

So what was the biggest, most luxurious ship in the early 1900's?  Here's a hint:

Recognize those four funnels (smokestacks) sticking out of the top?

You're wrong.  That's not the Titanic.  Darned good guess though.  And if you accept the information that's widely available, both in many books and most of the internet, the Titanic was the first ship to have an on-board pool.  Like so much information out there though, it's wrong.

So, if that's the first ocean liner with on on-board pool, but it's not the Titanic, what is it?  It's the Olympic, the first of White Star Line's three Olympic-class ocean liners.  It's also the only one to stay afloat for significantly longer than it took to get it built.  The Olympic sailed for over twenty years (despite hitting two other ships in its lifetime).  The Titanic, the second in the Olympic-class, sank on its maiden voyage after hitting an iceberg. The Britannic (rumour says it was originally intended to be called the Gigantic, no joke), the third and final Olympic-class liner, sank a few months short of three years afloat after hitting a mine during WWI.

All three of the Olympic-class ocean liners were built with very similar layouts and amenities, to the point that facts about the Olympic and the Titanic are often used interchangeably when it comes to discussing their layouts.  Some books have mistakenly printed blueprints of the Titanic when talking about the Olympic, and pictures that are said to be taken on the Titanic are sometimes pictures of the Olympic.  This is particularly true when it comes to the pool area, where the differences are extremely negligible and very few pictures exist from either ship.  Don't believe me?  One of these is the Titanic's swimming bath (as the pool area was called) and one is the Olympic's.

Can you tell which is which?
Click to embiggen, clicky-poppy

The Titanic is on the right, the Olympic is on the left.  Honestly, I thought at first that both were images of the Olympic being passed off as the Titanic (it happens, a lot), but then I noticed the tiny differences that, assuming the dates on the photos are correct, aren't likely to be due to additions to the Olympic.

 Alright, so the Titanic wasn't the first pool floating on the open seas.  That distinction goes to its older sister the Olympic.  It was, however, the first pool to sink into the open seas.

So did people like the idea of having a pool on their ship?  Well, the simple answer to that is, "Try and find a decent sized cruise ship without a pool nowadays."  Within a decade or so, pools weren't just common on the large liners, they were de rigueur.  And it all started with the RMS Olympic.

 The RMS Olympic pool: First in the on the open ocean, overshadowed by the first in the open ocean.

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Sources:
RMS Olympic image taken from here
RMS Olympc swimming bath image taken from LostLiners.com
RMS Titanic swimming bath image taken from CorbisImages.com


LostLiners.com
RMSTitanic.net
Last Mysteries Of The Titanic on YouTube.com
Titanic Wreck Observations 2005
Titanic-Titanic.com
Encyclopedia-Titanica.org
VictorianTurkishBath.org
National Museums of Northern Ireland
HistoryOnTheNet.com
Titanic-WhiteStarShips.com
Wikiepedia articles on the RMS Olympic and the RMS Titanic