I have heard lots of speculation about how the entrance of Fred Thompson affects the Republican primary race. The stories I have read and listened to focus on which candidate Thompson hurts. I think the interesting thing is who Thompson helps.
I think Thompson entering the race is a huge boost to Rudy Guiliani. At the moment there are several candidates all fighting to be the "true conservative" (generally defined in terms of social, fiscal, and defense policy). Guiliani can't do the normal social conservative business credibly so he has targeted his focus on economic conservatives and national security conservatives (and a social conservatism of a non-sexual sort as witnessed by his run ins with the ACLU in New York). He's done a pretty good job and probably can lock a lot of the Northeastern and Western Republicans (and quite a few "social conservatives" who are afraid of Al Quaeda attacking Peoria and/or like a "strong leader"). Meanwhile Thompson, Romney, Huckabee, and the midgets will beat each other's brains in fighting over the Southern and Midwestern voters. If the Social Conservative vote is fragmented 3-4 ways, Guiliani could win it all with a minority. Assuming McCain doesn't rise again I could easily see it happening.
The Republican party is in the middle of sorting out the lessons of the Bush administration. There is a sense thing have gone wrong and someone should be thrown under the bus. The loudest voices so far are the economic and national security conservatives bellowing that this is what happens when you let those Bible thumpers in the bus instead of under it. On the other extreme, you have Mike Huckabee and "the Party of Sam's Club" trying to find a Republican form of populism.