You can use copper to make watches and depth meters.
Those stay relevant...until you make a GPS.
I'd say keep 25 bars on-hand, just in case (ease of mind etc etc etc), and sell the rest.
gaming.stackexchange.com/users/28644/Christopher Berman
A few items and accessories require copper ore and/or iron, but for the most part, copper is of dubious value.
(Though usually so plentiful that anything you sell can be easily reacquired, if need be).
Copper ore is the most profitable item (as opposed to making something with it), as are all other ores except for Meteorite Ore (which should be sold as meteorite bars).
So sell with no regrets!
gaming.stackexchange.com/users/336/Raven Dreamer
Crafting the summoning items for hardmode bosses requires 5 copper and 5 iron bars.
The other ingredients may be farmed, but the metals cannot.
Unless you are absolutely certain you don't want to fight hardmode bosses and reap the substantial rewards, you should hang on to your copper and iron.
gaming.stackexchange.com/users/19827/kotekzot
In addition to what everyone else has said, you can also make two decorative items with copper, which for someone like me, means I need a lot of copper.
You can make copper chandeliers which are fairly cheap, but the biggest expense on my copper is making copper bricks.
1 ore per brick means that I'm farming up a whole lot of copper.
gaming.stackexchange.com/users/12087/Mr Smooth
Hang on to all of the copper all the way through the game.
IT can be used for bricks and Chandeliers, which are both nice looking blocks when creating a detailed build.
If you're not interested in building, keep the copper until you have killed the Mech bosses and have a watch or gps, after that you won't need it.
gaming.stackexchange.com/users/220319/Pythonbites
In Terraria I've managed to equip myself in  Silver Armor  and all tools are silver or gold.  I also have a large stockpile of copper and iron bars.  I know I can use some ores for potions, but is there anything useful I can do with the bars besides sell them?  If I sell them, would it be better to craft them into items first?
What can I do with all this copper?
gaming.stackexchange.com
<terraria>
gaming.stackexchange.com/questions/80026
gaming.stackexchange.com/users/121/C. Ross
You can use copper to make watches and depth meters as well as chandeliers and bricks. Other than that, it is of dubious value. Most use copper to craft specific items. Other than that, it seems there isn't  any special value to it.
It seems that most users use copper for decorative reasons. A user is suggesting to sell it. While few others propose to store it.