I know a lot of rabbanim remarry after the death of their wife, but are there any famous rabbanim who did not?
The Gemara indicates that a person who hasn't yet had children should marry someone who appears able to have children, so he can fulfill the mitzva of pru urvu. If someone already had children and is now single, we recommend that he remarry because the Torah says lo tov heyos ha'adam levado, it's not good for a human to be alone; but it's his choice whether to marry someone younger to have more children (ideal, as Koheles says "plant in the morning, but don't give up in the evening either"), or someone older who can't.
There's a cryptic passage in the Ramban's Milchemes Hashem that seems to indicate "it's not good to be alone" is also a biblical requirement, but it's generally understood as a very strong recommendation.
Nonetheless, plenty of great rabbis did not remarry after the death of a wife -- especially if he was no youngester, and she was a peer who'd been with him for a very long time. Neither Rabbi Menachem Mendel Schneurson nor Joseph Dov Soloveichik (both of blessed memory) remarried after the deaths of their wives. I don't think it was a halachic thing in any way, or even an "I hereby refuse!". They just didn't feel it was right for them. (Soloveichik said that when they put Tanya went into the ground, a lot of him went too.) We are all human and react to losses in different ways. There's no cut-and-dry answer on this one.
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