Never. (Note: new edits. As many more expansions have been released since I first wrote this answer, there's a lot more exceptions.)
Well, almost never. Don't buy copper unless you've got a strategy that will do well with it. Silver is almost always better than Copper, and most of the time, buying nothing is better than buying Copper.
You've got the Gardens exception in your question, actions that can be used effectively with Copper include Goons and Forager (thanks @John Robertson). As @Gendolkari comments, if your target buys aren't too expensive (say $5 or less), then Coppers can help you get there; this applies to Duke/Duchy, Gardens, Ill-Gotten Gains, etc.
I've seen new players make the mistake of thinking more money is better, so they'll buy a Copper with a left-over buy. This is obviously bad because it's the money in your typical hand that matters, not the money in your deck. If your hand size is 5, adding Coppers is going to reduce your buying power unless your deck is really bloated (maybe with Curses and Ruins). Players quickly learn to hate a hand full of Coppers when they want to buy a Province, and stop making this mistake.
It's much more common for somewhat more experience players to overestimate how good a Copper-using card is. Examples below: Moneylender, Coppersmith, Bishop, Mine.
Moneylender can be a great card, but some players will think it's a great card because of the $3: Moneylender shines in the absence of other trashers because it cleans your deck of Copper. Especially since Moneylender is a terminal action, buying several Moneylenders and then buying Coppers to feed them is not a viable strategy by itself. It requires 2 cards and an action to get $3; if you had two Silvers instead you'd have an extra $1 and an extra action to use. Spice Merchant is very similar.
With Coppersmith, there are decks in which it can work very well (@BlairHippo brings up Apothecary/Coppersmith), but it takes more than just Coppersmith. You need a lot of card draw for Coppersmith to work well, but card draw helps most everything so there are often more viable strategies on the board.
Bishop can convert Copper to VP, which is great. But anything costing $2 or more gets you more VP. You'd be better off buying Estates to feed to a Bishop than buying Coppers.
Mine falls in this category as well. What makes Mine a good action is that it gets rid of bad treasure, replacing it better treasure. If you then go and buy more Copper to feed to a Mine, you're missing the point.
Of course, if you have a bunch of activated Cities (lots of actions and cards) and a few Goons (lots of buys, rewards for buying), go ahead and buy some Coppers and Moneylenders/Coppersmiths/Spice Merchants etc., but if you've got a good Goon engine going your probably don't need much advice.