Resistor power ratings
Resistors commonly fail when asked to dissipate too much power - the permissible power is given in Watts.  The power dissipated in a resistor is determined by its resistance, and the currrent through it, or the voltage across it.

Resistors do also have a maximum voltage rating, which is independent of the resistor value.  All resistors of a given style (size and construction) will have the same power and voltage ratings.

I don't think I've seen a maximum current rating for a resistor.