What would my printer do if I set very big travel speed?
If a speed is set above the limits of the stepper, the stepper will stop rotating or stutters.
Basically there are 2 limits, the first is the limit of the board to generate the pulses to the stepper and second, how these pulses are processed by the stepper.
The speed of steppers depends on several aspects, including:
- microprocessor speed
- stepper driver
- micro-stepping setting
- voltage
- etc.
This reference gives you some more background as well as a table (which is a little optimistic for Marlin firmware) with maximum speeds. Depending on the application in your printer (stepper type, pulley size and microstepping value), it lists some maximum speeds for various boards:

What is maximum safe travel speed?
In case of an Anet A8, 1,8°; 16-teeth-GT2-pulley; 1/16 microstepping, this leads to 160 mm/s on Marlin on an Atmega microprocessor (note this is optimistic).
I currently use 120 mm/s. Is it safe to increase this value to 200 mm/s?
That depends. If you work out the mechanical and electronic details of your printer, you could look up the value you could ultimately use.
Is there any risk of damaging stepper motors if I set too big travel speed?
No there is not, the stepper will stutter or stop. I've had this with too fast retractions on an extruder stepper motor.