The Pulverizer from Killing Floor 2 (a sledgehammer with a "barrel" bored through the head, a firing pin, and a pump-action mechanism feeding from a 5-round mag, for shooting zeds while also bludgeoning them to death)
The infamous dildo-bat from Saints Row 3/4
The various pneumatic guns from the Metro series (practical yes, but very unconventional)
Javelin sniper rifle from Mass Effect 3, which fires a hypervelocity jet of ferrofluid
Halo's needler, heat-seeking explosive crystal shards definitely count as unusual