What can I do with all this copper?

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.

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!

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.

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.