There are a number of games based on Settlers of Catan. Most of the derivatives released fail to have the repeated playability of the original.

Seafarers of Catan
This game is an expansion to Settlers. It changes the game in small ways, although the presence of two robbers (the robber-baron and the pirate) can lead to serious amounts of eit being dumped onto a player. The gold resource tends to be a trifle unbalancing.
Knights and Cities of Catan
Another expansion to Settlers, this game focuses on the development of civilization, warfare, and fighting off barbarian incursions. The addition of advanced resources (paper, cloth, et al) and a tech tree tend to distract players from winning. The barbarians and knight combat are enjoyable, although the random effects of the civilization cards can lead to odd fringe cases.
Historical Variants - Cheops and Alexander
These are interesting "play once" expansion games. Alexander follows the conquests of Alexander the Great, with players vying for control of conquered land. This game involves a lot of bidding. Cheops has players building a pyramid in addition to normal play. Both of these play on static boards.
The Settlers of Nurembourg
This stand-alone game plays on a static board, with players vying for trade routes, and building inside the city as well as outside. A fun game once or twice; but there is a clear winning strategy for repeat players.
The Starfarers of Catan
The stand alone game takes the Catan series into space exploration. A wonderful variant, if a bit expensive (USD 75.00). There is a clear distinction between the early, mid, and end game. The addition of alien races to trade with makes for an interesting swap.
The Settlers of Catan Card Game
If you have nothing else to play, this is an okay game. But it doesn't resemble Settlers too much.

The Settlers of Catan Two-Player Variant

So, you want to play Settlers, but you only have two people. As noted above, the card game isn't great. Here are some rules for a two player game. Play with the normal rules except as noted.

Map Layout
Place the desert in the center of the island. Beginning at a point, and circling inward, place the number tiles in this order: A,R,K,B,P,I,G,Q,C,H,E,D,M,J,F,O,N,L
Initial placement
The first player places two settlements, each with an adjacent road. The second player places three settlements, each with an adjacent road, and takes resources for one settlement. The first player places one more settlement and adjacent road, and takes resources for it.
Robber
The robber is much more limited in this variant (otherwise, whoever builds a card factory is virtually guaranteed to win). When a seven is rolled, discard half your cards (rounded down) only if you have more than nine cards. Roll d6. Divide by two, round up. This is the number of hexes the robber can be moved from his current location. (If you are moving the robber by playing a knight, you can always move him at least two hexes). Every time the player who last moved the robber completes a turn on which they did not move the robber, move the robber one hex towards the desert. If there are two equivalent options, select randomly. Reroll sevens in the first three full turns of the game.
Victory
Victory is achieved when a player has 13 victory points.