Fresh fruit?
“Mad” Jack Churchill fought in WW2 and killed with a bow and arrow and his family Claymore.
Auxiliary policeare used in several countries, including Canada and India.
I don’t know if would count for this, but I remember a story about a soldier, maybe a marine, who had his great-grandfather’s dress sword. I don’t have any more info, but perhaps there are soldiers in other countries with longer military records than ours who may have a relic like that.
I’d look to primitive weapons such as spears, bows, blowguns still being made by tribal villagers and the like.
Quite frankly I think that looking at First World armies/police forces, especially the US army, is not going to produce a sensible result. Amongst government units the oldest weapons are going to be found amongst in third world countries. These countries are far more likely to buy, or be given, military surplus from more developed nations. This is where you are likely to find older weapons in regular use. WWII surplus BARs are still being used in SE Asia, or at least they were into the late 1990s.
The police forces in parts of Africa or Se Asia are probably even more extreme, basically making do with whatever they have to hand. In some cases the “police” are very informal militia and aren’t issued any weapons at all, so the local cop carries his own weapons, In those situations it’s entirely probable that we have police walking around with genuine WWI era Lee-Enfields or handguns.
But the real winner is probably going to be in more informal settings. There are plenty of people who own older weapons, whether rifles, handguns or shotguns, and carry them for self defence purposes. It wouldn’t be at all surprising that someone out there is regularly carrying a 110 yo revolver. They may not be firing it at people daily, but since nobody outside of a warzone will be doing that, I think we can include these deices as legitmately as a B52: its *intent *is for use as a weapon.
Does anyone actually read threads before posting?
Sex.
I regularly shoot several Mausers built in the late 1800s. They are old weapons, and I still use them as such, so they count.
Not traditionally, no; it spoils the now.
I wonder if there are enthusiasts who hunt using authentic prehistoric arrowheads?
You use them to kill people?
I believe the author of The Gun (a good read on the history of the AK-47) located at least one of the early made AK-47s currently in use (and working quite well) with a Northern Alliance fighter in Afghanistan.
I know wilderness survival types who do this. I don’t know how widespread the practice is, but I think it’s kind of neat. Their hunting club has brought in large catches of game including big bucks (deer) with handmade weapons.
my first post on this board
I didn’t read the whole thread, but I was thinking maybe a Bowie Knife would at least be in the running. Still being made and most likely still being used.
Shut up!
For example:
http://www.practicalprimitive.com/tracking.html
For a loose definition of “people*,” sure, what the hell. 
*“People” here being defined as computer monitors, law books, beer cans, paper targets, iron pipes and anything else I can find to potshot at out in the desert.
I recall reading that during the early stages of the Soviet-Afghan war, even more ancient weapons were used by Afghan fighters, including the occasional family flintlocks.
On a more recent front, old Soviet/East German supplied working Stg.44s have been found/captured in Iraq…and Syria, this year.
These rifles aren’t 100% ancient, but as the wikipedia article says: “Some of the parts used may date back as far as the 1890s.”. I’m sure some Mosin-Nagants where the whole gun is ancient are in use somewhere still.