It depends on your supply voltage. You have to be able to overcome the cumulative forward voltage of the series combination in order to get them lit. As an example, with a 12 VDC supply, you could drive up to five red LEDs (2.1V @ 20 mA) in series. The current isn’t used in the calculation: 5 * 2.1V = 10.5, which is less than 12, but 6 * 2.1V = 12.6 which is over 12, so five is the maximum series combination for that type of LED at that supply voltage.
When you need more, you can build arrays by combining multiple series strings in parallel. In that case, your load current needs to be calculated and kept lower than the rated supply current. For a given number of LEDs in a series+parallel array, using the largest series combination possible will keep the total load current lowest.