The Atmega328 chip used in many Arduinos has a limit on the amount of current it can provide directly. You can find this in the datasheet section 28.1 page 313.
- A limit per pin - 40 mA max.
- A limit per IC total - 200 mA max
simulate this circuit – Schematic created using CircuitLab
If you are using the Atmega IO pins to turn on transistors (FETs or BJTs) and use the 5V or 3.3V supply to provide current to the LEDs through these transistors then there is no problem with the Atmega328 current limits.
simulate this circuit
FET circuits are simpler. For larger numbers of LEDs it may be better to use a suitable LED-driver IC instead of using large numbers of transistors.
The voltage regulator on the Arduino board that is providing regulated 5V or 3.3V power will itself have a limit which may also prevent you using it to drive a large number of LEDs (or a lower number of high-power LEDs).