I wonder whether I ........ ever see him again.

In this sentence, the phrase "I wonder whether" introduces an element of uncertainty regarding the possibility of seeing the person again. The use of "would" in the blank is appropriate because it conveys a sense of conditional or hypothetical future action. It suggests that the speaker is uncertain about whether they will or will not see the person again, making "would" a suitable choice for this context. This word choice acknowledges the possibility of the event happening but does not commit to a definite future meeting, which aligns with the sense of wonder and uncertainty expressed in the sentence.