I believe the Newcomb's paradox is a significant problem in philosophy, since I regard it as a well formulated version of the lazy argument (under certain conditions) with real life implications.
Here is the original problem: There is a predictor [who is never wrong], a player, and two boxes designated A and B. The player is given a choice between taking only box B, or taking both boxes A and B. The player knows the following:
Box A is clear, and always contains a visible $1,000.
Box B is opaque, and its content has already been set by the predictor:
If the predictor has predicted the player will take both boxes A and B, then box B contains nothing.
If the predictor has predicted that the player will take only box B, then box B contains $1,000,000.
The question is, what is the rational choice, taking only B or both A and B.
Now consider this practical variant of the experiment. Instead of the predictor, there is an honest person who promises to fill box B with $1,000,000 if and only if the player chooses only B, and he will do this after the player has made his choice.
I believe in this variant, it's common sense that the rational decision is to choose only B. Now, if we assume that determinism is true, then the content of B is already determined before the player makes his choice. This seems to be equivalent with the original problem. How come choosing only B is not much of common sense in the original problem?
Bonus: I believe the same can be said about the lazy argument. If the predictor has predicted your grade in the tomorrow's exam and has written it on a piece of paper, it seems controversial whether you should study or not. Assumption of determinism also implies your grade is already determined. However, it doesn't make the decision about studying that controversial.