What are the differences between the four editions of The Settlers of Catan base game?
The new fourth edition has a few minor changes in appearance, and the biggest change is a new set of border pieces that surround the hexagon tiles to keep them together.

The most important thing to know is that they do not mix and match very well: if you have the 3rd edition of Settlers, you should buy the 3rd edition of the expansions.  If you have the 4th edition of the base game, you should buy the 4th edition expansions.  So if you're just getting into it, I would suggest buying the new edition, since the corresponding expansions will be easier to find.