This topic has been discussed previously - in this thread I am summarizing some of the data, and cross-referencing previous discussion on this subject.

Clearly Settlers of Catan is subject to some major randomness on account of the dice-rolling, and it can have a significant impact on the game. Statistically this will even out over the course of many games, but within one game, it is possible to have "poor luck" and have your statistically "high" rated number (like 6 or 8) rarely get rolled. Consider this graph, which charts the results for 100 simulated games consisting of 75 rolls each:

http://www.aldaron.com/sciencegames/2d675.gif

Statistically dice perform with a probability of 1/36 per roll, but over the course of a single game the actual rolling won't accurately reflect the statistical probabilities since the sample is too small - as is clear from the above graph (although perhaps the rolls over 1000 games would be accurate).

What are the solutions? There are at least three:

1. "Deck of Dice" Settlers of Catan Variant
Description: Instead of using two dice, use a 36 card "deck of dice", with a card for each possible dice roll. You then work your way through the deck, which is naturally shuffled at the beginning of the game (and for variety: re-shuffled when a "reshuffle" card is turned up).
Reason: This ensures all numbers turn up according to the statistical odds, and can enhance strategy (eg if no eights have come up after five "rolls", you know that there's a higher probability of getting one of the 7 (out of 36) eights in the rest of the game, and can plan accordingly).
Evaluation: As others have shown, while this solves some of the random aspects of the game, it creates new problems related to card counting and the effect of the robber. In short, not a feasible solution, because it creates more problems than it solves.

2. "Foodstamps" Settlers of Catan Variant
Description: Whenever a player does not produce anything in any given roll, he is given a foodstamp token. He may trade in a number of these tokens (equal to the number of visible points that player has) during his turn for a resource of his choice.
Reason: It mitigates poor luck and helps less as a player's position becomes stronger.
Evaluation: This is probably the best solution for people looking to reduce the randomness somewhat.

3. "Original" Settlers of Catan
Description: No change to the existing game.
Reason: When you undertake to play a game of Settlers, you are accepting the randomness as part of the game! Sometimes it will help you, other times it will work against you, and this is something you accept by playing the game.

In short, randomness certainly is part of the game. Either you can accept it as such, and enjoy the game for what it is, including the random element. And if you don't like it or want to reduce this aspect, then opt for the "Foodstamps" variant.

For more discussion about randomness in Settlers, and some solutions, see these threads:
http://www.boardgamegeek.com/thread/6717
http://www.boardgamegeek.com/thread/6585
http://www.boardgamegeek.com/thread/25748
http://www.boardgamegeek.com/thread/68410
http://www.boardgamegeek.com/thread/84619
http://www.boardgamegeek.com/article/446938

You should also mention the drawback for foodstamps: It encourages players to build on all the same numbers, instead of diversifying. So, while it does artificially even the rolls out a bit, it simultaneously causes the effects of the die rolls to have very high variance.

Does 1/3 of a free resource per turn really encourage the development of a Catanian welfare state? I can't say its enough to drive me to avoid getting resources on production rolls which can produce up to 18 times more resources.

I'll take option