The Basic Game has been supplimented by several expansions:
Inns and Cathedrals (aka The Expansion) ; Builders and Traders, River II, Count of Carcassonne, King and Scout, and The Princess and the Dragon. And Rio Grande Games has recently brought out The Tower and a "Big Box Set" with the basic game, the River and the four major expansions has also become available.. These expansions add additional tiles, pieces and/or ways to score points. Some other tile sets are also available in Germany, adding a variety of lakes, mountains, etc. (See below)
Other "Carcassonne" Games which are not played with the Basic Game include The City, The Castle, The Discovery (a stand alone version), Ark of the Covenant, and a stone age variation: Hunters and Gatherers.
My family set has become "customized". It includes the basic set with both rivers, the three expansions: Inns, Builders, Dragon, as well as the King & Scout and Count of Carcassonne mini expansions. To this I have added the 24 Lakes and Fishermen tiles by Carsten Engels, and six homemade Fish tokens, which we use like the trade goods tokens in the Builder's set, these are given to those completing lakes with tiles that have the fish pictured on them. Starting with the King and Scout mini-expansion, I have added the Landlord and Friar tiles (which used the rules of Knecht und Bettelmönch (Laborer and Mendicant) by Christoph Berger) and created our own variant King/ Robber Baron/ Landlord/ Friar. I have added a few other tiles to our mix as well, gluing them to the H&G tiles in the King and Scout set. They include, for the river, an estuary piece (which must maintain an "untiled" outlet to the sea); and an all grass piece. We don't usually play with all the expansions. I have a page of the additional rules (pdf) and a page of Scoring tables (pdf) to reflect these additional expansions as well, as a compendium of our house rules with the various expansions and variants worked in. I created a Player's Reference Card to assist in us play and scoring as well.
Some other Expansion Tiles are available:
