A while ago I was playing a lot of two-player Settlers of Catan. I apparently wrote down the house rules we were using. The idea behind them is to make things fun while attempting to preserve game balance.
Starting Hand
Give a player resources cards for both settlements laid during the setup phase of the game, rather than the last settlement laid. This will make the beginning of the game progress a bit faster. Since resources are only being accumulated by the limited rolls of two players, the game tends to drag.
Robber
In a two-player game, you end up stealing from the same person again and again. An alternative is whenever a 7 is rolled, to re-roll the dice and place the robber in a hex corresponding to the number rolled. If the number rolled has multiple playable hexs, its the players choice on where to place the robber. If a 7 is rolled on this re-roll, the robber returns to the desert.
After the robber has been moved, if an opponent has a settlement or city on that hex, the player may steal a card.
This rule supercedes the requirement that a robber is moved into a position that affects a player, and cannot be moved to the desert (if the above option to move to the desert is used).
"Phantom" Players
This alternate rule is best played in the absence of other house rules. The purpose of the phantom players is to provide the limitations that other plays would impose (resources, robber, board layout) while providing for the potential resource gain of having those additional players.
Initial Setup
Each player rolls to determine who places a settlement first, herein known as the "First" and "Second" player. The second player first places a settlement of a phantom player on the board. The the First player places their first settlement, followed by the second player of their own settlements, followed by a settlement of the other phantom player by the first player. This order is reversed as per the rules, with each player placing a settlement of the phantom player they did not place in the first portion. Basically, each player should place both of their own settlements and roads, as well as one of each of the phantom's settlements and roads.
For example, Player 1 is playing red and Player 2 is playing blue, with phantoms playing orange and white. Player one won the initial die roll. The order would be: Player 2/Orange, Player 1/Blue, Player 2/Red, Player 1/White, Player 2/White, Player 2/Red, Player 1/Blue, Player 1/Orange.
Game Play
Between each real player's turn, a phantom player should be rolled. Resource cards distributed as appropriate. If a 7 is rolled by a phantom, the dice are rolled to determine where a robber moves - if a 7 comes up on the placement roll, the robber returns to the desert; if the robber is in play and the same number is rolled, the robber moves to the other tile (if available) or back to the desert (if there is no second tile).
Other than die rolls, the phantoms do not collect resource cards or participate in any way.