.30 cal aircraft machine gun, loaded with blanks, in the wing of a replica torpedo bomber which had been used in Tora, Tora, Tora.
I once got to fire off a few rounds with a .357 Magnum (Blackhawk I think)… that was cool.
When I was deeply involved in martial arts training I used a variety of weapons and became quite adept at using nunchuks, long swords, tonfa, and the bo (staff).
I used to carry a custom made set of nunchuks with shortened handles and a longer chain, they would fit right up against my forearm and could be withdrawn very quickly from under my sweatshirt or jacket. I remember working at my friends store one night and a guy came in and tried to rob the place with a pocketknife.
I can’t say I didn’t warn him…
would a fencing foil count?
as far as actually offensive intent, my best rounds are usually standard-issue rocks and sticks. (i have surprisingly good stats with a throwing stick.)
lachesis
Let’s see… M-16 (several variants), Galil (Rgular and carbine), Uzi, FN-MAG (AKA M-240), Minimi (AKA M-249), .50" Machine Gun, 52mm mortar, and 60mm mortar. I’ve also fired dummy rounds from the M-203, LAW and PG-7 - they don’t go boom, but firing them is more or less the same experience.
Oh yeah - granades, too, lots of them. Frag and smoke.
A fully automatic scaled-down replica of a Gatling Gun (the electrical self-rotating kind mounted in helicopter gunships, not the WWI crank models) made to shoot .22 rounds. Oh, you just have no idea the fun of sawing through a row of water-filled milk jugs unless you’ve done so.
Yes I’m one of those former military types and I like things that go BOOM
Since I was in the artillery firing big guns was an everyday thing.
M110 an 8inch SP artillery peice fires 200lb rounds. Amazingly accurate but definately NOT user friendly made a nice BIG BOOM, two actually. Since they’re no longer in active service, thats the most exotic.
M109 a 155mm SP artillery peice. It fires 100lb rounds not quite as Big a Boom but more user friendly and it provides a place to work out of the wind, rain and snow.
Beyond this the common stuff every soldier fires.
M-203 grenade launcher
LAW M-2 .50 cal. M-60, M-16.
But my all time favorites, the few live grenades and live Claymores I’ve used. Nice up close and (anti)personal BOOM.
Inky-, I officially envy you now. 
An early Napoleonic smallsword, circa 1807.
I didn’t use it in combat but I did put it through its paces. I still sigh when I think about the brief time I held it. It is a magnificent weapon.
Hmm, my navy model Colts are pretty sophisticated. Revolving cylinders, built in ramming lever, much less weight than the dragoon and Walker models, mild recoil and the outstanding ergonomics preferred by expert pistoleros from “Bill” HIckock to well, me. Not as much punch as the .44 caliber guns but it gives me the competetive edge. I call it “the original point and click interface.”
Oh, I’m guessing you mean weapons designed less than 150 years ago. Okay, those are good too. Since I never handled small arms in my military career it would have to be the H&K MP5K PWD. It’s the same as the MP5K carried under the coats and in the briefcases of the best secret service angents but has a fast open folding buttstock. A friend owns one and lets me shoot it in competition when I tag along. It’s a runty little sucker but the light weight makes it as quick as a handgun but with the precision of a carbine and the vertical “K” foregrip makes for excellent control. His is specially configured with a non-standard trigger pack. Positions are safe, single, two shot burst and rock&roll. The two shot burst seems to put the highest percentage of shots on target in the shortest time.
Look at that - firearm after firearm. But only two swords and two sticks. Who’s exotic now? 
A flame thrower, made my own napalm too.
I have never used a weapon against someone, but I have trained with the manrikigusari which at least sounds exotic.
Cheers, Bippy
I once beat someone unconscious with a standard rotary dial phone. My childhood was vicious.
6 1/2 lb broadsword.
I’ve shot a 54 caliber black powder muzzle loading rifle (cap and ball)
a .22 pump action rifle (not exotic, but weird)
a potato cannon.
my Replica 15th century Scottish Claymore…
my Viking axe and spear…
my various SCA weapons and tactics…
Roman gladius (sword) and scutum (sheild)…
Civil War rifle…
held a 14th century firelock…
actually foiled a beating by squirting my assailant in the eyes with Tobassco sauce “Nobody beats me in my kitchen!” …
more as I remember them…
I train with a bokken.
.50 caliber flintlock rifle
.45 cal cap-and-ball pistol (Arr, matie!)
Potato cannon
Wrist rocket slingshot
.444 marlin lever action hunting rifle
various shotguns and .22 rifles
Held a Japanese 7mm sniper rifle and Italian 6mm carbine, both WWII vintage.
Various compound and recurve bows.
Redeye shoulder-fired anti-aircraft missile, precursor to the Stinger
HAWK anti-aircraft missile (video in link)
Litany of USMC infantry and Stinger stuff (hand grenades, CS grenades, M-16A1 and A2, M1911 .45 cal pistol, M9 9mm Baretta pistol, Mk19 automatic 40mm grenade launcher, M203 40mm grenade launcher, M2HD .50 cal machinegun, M249 5.56mm automatic rifle, M60A2 and A3 7.62mm machineguns, and the M3 .50 cal machinegun, mounted on the Avenger Weapon System (Stinger missiles in pods monted on a modified HMMWV), pugil sticks, bayonet, and Kabar)
Compound and simple bows, slingshots, and a bolo (not used well).
9x18mm Makarov pistol
K1A1 Korean M-16 style rifle
SKS Russin 7.62 rifle
AK-47 assault rifle (Chinese)
Then the normal couple of general use rifles and pistol (.410, .20, .16, and .12 ga shotguns, .22, .32, .38, .357, and .44 cal pistols, .22LR rifle)
I have used, poorly I might add, nunchuks. Ouch.
My father is a Federal Firearms Dealer so I shot every kind of gun known to man growing up. The most exotic were a fully automatic Uzi with silencer, a fully automatic Mach 10 submachine gun with silencer, an M-16, the working cannon that was in our front yard, and my very own blowgun. We literally had dozens of rifles and handguns at any one time that I was free to shoot whenever I wanted. It was a good house to live in if you were a boy and liked things that go BOOM.