Option is a chain of contracts which means there are many strikes. For exchange traded options, such as equity option, usually the strike is the multiple of 5 (5, 10, 15...) for some interest rate options such as Eurodollar futures option the strike is listed with an interval of 0.125% (0.125%, 0.250%...) and for the options that is deep in or out of money the exchange may offer contracts that has a larger strike interval. E.g. 0.5%.
For OTC traded options, such as cap, floor or swaption, the strke is quoted in for example:
-200 bp -100 bp -50 bp ATM +50 bp +100 bp + 200 bp
Since they are issued on a rolling basis.
If you consider some structured products issued by banks with only one strike, the story is more complicated. Sometimes they will choose a strike that is acceptable for risk management. They will calculate the probability that the underlying's price is higher or lower than the strike. Sometimes that will use strike to adjust the over price level of the product. But in most times they will set a integer strike and adjust other parameters to make the product either attractive to the investors or beneficial to the banks. But in general, this issue varys by different cases.
Best,