The great steam liners of the first half of the 20th Century had four typical fates. Looking at Titanic and her sister ships gives insight into these. Titanic was, of course, sunk by natural causes, colliding with an iceberg in 1912. This was rare - these ships were generally big enough to survive the storms of the Atlantic, and iceberg collisions were rare.. Accidents were somewhat more common, with the Andrea Doria and the Empress of Ireland being good examples of ships sunk in accidental collisions, while the Queen Elizabeth ultimately sank in a fire. The next sister to be sunk was Britannic. She was launched in February 1914, and completed as a hospital ship for the RN in WWI. In 1916, she would be sunk by a German mine in the Mediterranean. Liners served in a variety of roles in wartime- as well as their usual role as passenger carriers, they were used as troop transports and hospital ships. This put them under threat; as well as Britannic, other liners sunk in WWI or WWII include the Lancastria, sunk by aircraft in 1940, and the Lusitania and the Athenia, sunk by submarine in 1915 and 1939 respectively. Those that survived either of these fates typically suffered that of the other Titanic sister, Olympic. She was laid up in 1935, as newer ships and reduced demand reduced her utility to Cunard. She was put on sale for five months, but was ultimately sold for breaking up. She was towed to Jarrow, where her superstructure was demolished, and in 1937, she was towed to a yard in Inverkeithing for scrapping. Her scrap was melted down and recycled, as it was with other scrapped ships of the period. Most liners that escaped sinking would end up in a shipbreaker's yard being slowly torn apart. A few would escape this - Olympic nearly did, as a consortium sought to buy her and turn her into a floating hotel in the south of France. However, this cost more than most investors were willing to put forward. The Queen Mary, now in Long Beach, is one of the few to survive in this form.

The Titanic was one of three Olympic Class ships built by the White Star Line. The other two were the Olympic and Brittanic, both of which were similar to the Titanic in size and luxury. The Brittanic continued it's use after the disaster of the Titanic, and was evenutually requisitioned by the British government in WW1. Major changes were made to both ships, and there was an improvement in safety protocols and communications, and an increased number of lifeboats on all ships. It was struck by a torpedo off the coast of Greece while serving in this capacity. Most of the men were saved on this ship. Olympic had a similar history, although it survived through WW1. The Great Depression greatly reduced demand for interoceanic transportation, and in 1934 the Olympic had a minor accident with another boat. The Olympic was succesfully evacuated, but given the age of the ship and the economic conditions, the ship was scrabbed. The fittings were sold off at the time, and many of the light fixtures, fireplaces, etc are still in use throughout the world today. Go to the White Swan Hotel in Alnwick, and you can eat at the same tables that people did on the Olympic!

Others have answered what specifically happened to some of these ships, but I just want to point out something from your question. Ships like the Titanic, while having luxuries for their first class passengers, were not primarily luxury cruises. They were primarily made to carry third class passengers in large numbers, with the purpose of making such giant ships being to cut costs by carrying as many passengers as possible in a single trip. However, as practically all of the third class passengers were immigrants, the passage of a series of laws in the US culminating in the Immigration Act of 1924 drastically reduced the amount of third class passengers and made it unprofitable to maintain these giant ships, so they were slowly phased out.