They die.

Well, I haven't ever played a character through to retirement mostly because I love to have them die gloriously in battle saving their friends. But if I did ever make it, I'd probably have them do these things (depending on what kind of character [Basic D&D classes]):
Cleric: Either go back to where he came from and spend his time worshiping his deity, or move somewhere new and build a church dedicated to aforementioned deity and start a large charity organization for the poor.
Fighter: Build a kingdom, not let many people know that he is king and have one of his trusted friends (maybe an old adventuring companion) rule while he opens a tavern at which he spends all of this time talking with passing travelers and serving drinks.
Magic-User: Build a tower for himself a few miles from a town that is open to anyone interested in Magic, and donate a large sum of money to the town for a huge library.
Theif: Probably start a theives guild in a small town while slowly giving money to the down to help it grow and expand, bringing in new business for his guild.
Dwarf: Retire back to his homeland and be content spending his days working at the anvil making beautiful and powerful (he's rich by now... He can afford all of the best materials) weapons and armor to sell very cheaply to young dwarves getting ready to go out into the world.
Elf: Buy a huge lot of land containing a forest and creates what is much like a giant inn for travelers, free of cost to stay but instant banishment if they harm the forest or anything living there.
Halfling: Finds a nice quiet town near a lake and buys a nice home on the lake front and spends his days relaxing, eating, fishing, and remembering his adventures.
Gorilla