Fat Man/Experimental MIRV (Fallout 3). I could never master the art of not blowing myself to smithereens with this thing, and the ammo's too valuable to waste when you can sell mini-nukes for 125-225 caps (depending on barter skill). One MIRV shot and you've just wasted over a thousand caps. (but, as someone else pointed out, in god mode it looks COOL.)
Missile Launcher (New Vegas, but only in Hardcore Mode.) I don't have much use for a slow-firing weapon that has ammo weighing 3 pounds a shot---even with 10 STR and Strong Back, there are just too many other things I'd rather be carrying around the Mojave. Again, though, this only applies to Hardcore Mode where ammo has weight. But I wouldn't play NV any other way.
Sniper Rifle (New Vegas). Nerfed to hell and back in the patch. It used to be a good intermediate step between the Hunting Rifle and the Anti-Materiel Rifle for a Guns character, but now you're better off just hanging on to the HR with a scope and the other weapon mods until you can get the AMR.
Note that I'm not counting pea shooters like the .32 pistol, Chinese pistol, and other stuff that exists primarily as vendor trash in Fallout 3 (or, for that matter, the .22 pea shooter pistols in New Vegas).