Chopsticks (the eating implement, not the piano piece… although it might qualify, too).
You mean a spurtle? 
The Zippo lighter doesn’t seem to have changed much since it was introduced in 1933.
Hook and loop fasteners? Although we call them “Velcro” the design is the same today as when ancient cave peoples used hook and loop fasteners on their animal fur clothing.
Point of clarification: It seems to me that people have been interpreting the OP two different ways: (1) Taken most literally, I don’t think anything suggested so far has actually “never been improved upon or modified in any way”. (2) However it seems to me that some items have been improved or modified, while the original design is ALSO still current. For example, while it is true that recent years have seen the plastic-coated paperclip, many (perhaps even most) are stillof the plain metal variety.
I would also note Jayjay’s post, with the link to competing designs of paper clips: A third interpretation of the OP could mean that the original design was not necessarily NEVER modified, but merely that we’re looking for products whose last modification was a very long time ago. (I’d also point out that the “Ideal Paper Clip” in Jayjay’s link is still easily available today.)
Can you describe that product a bit better? In my imagination, cave people may have had “hook and loop fasteners”, but each hook and loop would be fastened individually. Velcro(R) is an entirely different product, where the whole point is that all one needs to do is to press this surface against that surface, and all the hooks and loops fasten themselves.
^sorry, whooooosh.
It would be a pointed stick.
I’ve yet to see a Coin Star Machine that didn’t look like a Coin Star Machine.
sewing needles, though the options for what it’s made from have expanded.
The P-38 can opener first introduced in 1942 is still handed out by disaster relief agencies today. It’s long been cited as an example of good practical design.
This is square on the nose. Thank you sailboat.
Must be more, no?
my thought process: hoola hoops -> wheel -> merry-go-rounds -> recipe for cotton candy -> thong sandles -> screwdriver.
How about the button; the basic disc with two holes still serves. Seems to me different colors and sizes materials and such are simply stylistic changes, not changes in design … and bone and wood have been used for a very long time.
Two kitchen products came to mind for me - The KitchenAid blender and Waring mixer. Both are essentialy unchanged since they were first produced - the form of each is the same regardless of fashion trends, and they are both successful and popular in current markets.
Mittu:
What about when it developed eyes and became “helpful”?
Exactly mine, too, as soon as I read “hoola hoops”. Although after a couple more steps, I ended up -> Platypus With A Hat.
But are you sure you want to tell everyone on the internet how your brain works?
The British Land Pattern Musket (aka the Brown Bess) was the official issue of the British army from 1722 until 1838. And there were still some being used in combat as late as 1879.
The dildo.