None?
Economies can be built using currencies other than coinage. Even assuming (as you imply) we are not talking about a time when digital currency is practical, there have been times when exchange was based on weights. And before you argue that just changes the problem into how many weights you need, I'll note that sliding-countermass scales and spring scales don't have this issue.
Also, as per comments, this is assuming you even have currency as such. While it's true that something which served as "currency" has been pretty common throughout history, its use depends on at what level of the global economy you are looking. States, or well-traveled individuals might use currency, but individuals within a small community might operate entirely on barter, and may not even accept currency. (What good is a coin, after all, if no one accepts it as payment?)
But more practically...
There is no good fixed answer. Rather, coinage tends to develop into whatever denominations are "convenient". The reason we have denominations is because it's awkward to pay for a car using a million pennies, both in terms of carrying them around, and in terms of counting them out in order to complete a sale. You want your smallest coin to be about the value of a very inexpensive item, but more importantly, to be a value that most people won't care about an item's cost differing being more or less by that value. Many would argue that the US penny is too small.
Once you have your smallest coin established, you want coinage in larger denominations up to an amount you would expect someone to pay cash rather than using a bank note of some sort (think "check", not paper money; for our purposes, paper money and coins are roughly interchangeable). These denominations should strike a balance between making sense in your counting system (e.g. 130
why coins tend to divide larger decimal numbers nearly) and minimizing the number of coins. For example, if we had coins strictly in powers of two, it would minimize the number of coins in any transaction, but humans don't like dealing with powers of two and it would actually maximize the number of different coins.
In this respect, having a base-ten number system is a disadvantage. A species/culture with a base-16 system would almost surely have only coinage at powers-of-four values, since this is a pretty good "sweet spot" between not needing more than a few of any specific coin for a given sale, and denominations that neatly round up to "whole" increments of larger values (that is, values consisting of a single non-zero digit followed by some number of zeros). Five would also work well, but most humans don't think in powers of five, which is why we wind up with tens (and twos, like the \$20 and \$2 bills; the latter is real, if almost never seen in practice). But using only powers of ten would mean needing up to nine of a smaller coin, and that's getting to be a bit much.
A more practical system — assuming your culture uses base-10 — might be to alternate fives and fours (with twice as many fives as fours). We sort of have this with nickels and quarters, and with \$5 and \$20 bills. It's not hard to imagine eliminating dimes and \$10 bills, in which case...
Seven
...pennies (1¢), nickels (5¢), quarters (25¢), dollars (\$1), \$5, \$20 and \$100 are probably sufficient. (For values above that, people will probably want to involve accountants rather than paying out of cash-on-hand. Keep in mind this also assumes that a penny is actually worth something. Also, don't think of these as directly relating to real currencies, or as literal "coins"; I'm trying to address your question which was about types of currency. "1¢" might be a chunk of a coin that has been cut into bits, where doing so is common enough to be an accepted way of "making change". $100 might be a brick of silver or gold; not something you'll see every day, and indeed something many people will never see in their life, but not so large that no one wants to ever deal in them directly.) 855