I don't have one for Fallout, but for TES, it depends on the sort of character I am playing:
If it's a fighter, then I love the Longhammer.
If it's a mage, then I have to go with a good destruction staff.
If it's a stealth character, then it's the Razor of Mehrunes Dagon or the best craftable bow (the Nightingale Bow is glitched.)
For TES it's the Nightigale Bow. Ever since I saw it for the first time on Karliah's back I asked her: So when are you going to give me that bow?
For Fallout on the other hand, I love modding stuff and I'm proud of the gun names I came up with.
This is inspired by Robocop's (Alex Murphy) famous weapon. Basically, for anyone facing the barrel, if anything can go wrong, it will go wrong.
It has nothing to do with the superhero. It's just that most of the times I don't use a shotgun in shooters. I tend to get killed more often the closer I am to my target, hence my favorite weapon is the sniper. With Fallout 4 however I found out that this is no longer the case and a shotgun is very, VERY useful. Every time I charge at someone with it I feel like a daredevil.
Ah yes, this is my favorite weapon in Fallout 4 because A) I made it into a sniper; and B) it has huge sentimental value. Last time I modded it, I added the recon scope. I don't know if I'll keep the mod or not because I haven't tested the new version in battle yet. I'm starting to get the hang of nailing heads to the wall. A spike's mid-air low velocity is a b*tch.