The content is accurate at the time of publication and is subject to change.
I'll give you a warning straight away: there's no direct answer. In fact, here's a spoiler: as many as you can manage. However, if you want the ins and outs of estimating the right number, let's delve into the depth of credit card management.
How Owning Credit Cards Affects your Credit Score
To start with the basics, let's determine what influence each consequent credit card has on your credit. There are two main parameters that are affected when you open or close an account: your credit history and utilization ratio. Credit history shows how much experience you have in terms of borrowing and payments. It is usually calculated as the average age of your open accounts. The longer your history is, the more likely the banks are to approve you another card. As for the utilization, it is the ratio of your total balance to your total credit line. It is a given that banks prefer a utilization ratio no more than 30%, so if you have $10,000 credit limit on all of your cards combined (say, $1,000 $3,000 and $6000), you shouldn't carry more than $3,000 of a balance.
So, if you have several credit cards that you use moderately and for a long period of time, you'll benefit more than having just one, because your history will be longer and the cumulative credit limit will lower your utilization (if you don't max all of them out, of course). What happens if you close a card?
If it's a new one with a small credit limit, you won't lose a lot. If you've had it for a long time and manage to get a substantial credit limit, it's going to bite off a massive lump of your credit history and increase your utilization, so expect a drop in the credit score. On the other hand, if you open an account, a bank pulls a hard inquiry, which causes your score to dip a little - only a few points, not enough to really worry.
How You Should Act
If you are new to credit card business, then your goal is building a credit score. In this case it's best not to squander your energies and devote your efforts to maintaining one credit card. As soon as you stand on your feet well, you may think of obtaining one or two more.
Yet if you have multiple cards at hand and don't know whether to close some accounts or get more cards, then it's more complicated. Closing accounts by yourself doesn't seem like a nice idea, since it will hurt your credit score, but unused accounts might be closed by banks themselves. What to do? Make a small purchase once in a while (even as rarely as once a year) and pay it off immediately. Then again, having a lot of accounts is difficult to keep track of. If you feel dizzy at the thought of all your due dates and statements, set up an autopay, or if it's just too bad, wait for the banks to close the unused ones.
Remember that credit cards are not free money, it's the money that you earn anyway, only given beforehand and more conveniently. So, don't use more money than you are able to pay in time. Large credit limits are destructive if don't know where to draw the line. Think of them as more of an insurance in case you need something urgently and a good front for the bank if you need a big loan or a mortgage.
Generally, the reasonable number of cards that people are able to track and manage is somewhere around 7, but, as you have already seen, it depends on your capabilities and goals. Speaking of the latter...
The Ultimate Strategy of Getting the Right Number of Credit Cards
Why would you actually need several credit cards anyway? Isn't it enough to have just one for all of your purchases? The answer is no. If you really want to benefit from using credit cards, it's wise to have different ones for different purposes. In fact, travel hackers use a strategy of churning credit cards, which is getting several, mostly for sign-up bonuses, and then closing accounts before paying annual fee and getting them again. Thus they manage to rack up thousands of points and miles. Anyway, not only does chasing up points take a lot of time and energy and it's probably not what you are ready to devote your life to, but banks have clued into it and limited welcome bonus offers only to the new accounts. We would certainly advise against it, as it is a good way to lose all good relations with a bank.
The Bottom Line
To sum it up so far, the number of credit cards that is right for you depends on how many you can manage and how many really serve your goals. The way to know that too many cards for you is when you are lost in your bills or you have a big debt. But if you are sure that you can use all these cards to your convenience, you can definitely take several and benefit from them.