BJT - absolute maximum base current?
The 2N3904, presumably the same die, lists maximum peak base current as 100mA. 

Since that presumption is not necessarily correct, I would suggest limiting peak current to a fraction of that (maybe 20-50mA) and continuous base current to maybe 20mA (1/10 of the maximum collector current). 

Remember to take the power dissipation due to the base current into account- Vbe can be in excess of 1V at higher currents, so it will be significant in an SOT-23 package. 

Looking at similar parts that I tend to use, the MMBT4401 is specified at 50mA base current and has 1.2V Vbe(max). The MMBT3904 will have a higher Vbe drop. The 8050 has a 1.2V Vbe(max) at 80mA base current (again the MMBT3904 will have much higher Vbe drop). 

There's generally no point in having more base current than about Ic/10, so I would say that determines the minimum practical base resistor. If you're switching a 100mA relay coil using a 5V drive then the minimum practical resistor is about 400 ohms, which is well below the current that would likely cause long term damage, let alone immediate damage. 

Note that the absolute maximum is not a target you should aim for, it's a warning of something specified by the manufacturer that you should stay well away from if you want reliability and should look carefully at the measurement conditions in case they are optimistic (for example, if abs max of something is specified at 25°C and your application sees 80°C you may have to derate the number considerably to be safe). 

If there is no abs max of something specified that doesn't mean you have carte blanche to go as high as you want, it simply means the manufacturer didn't think it was important specify it, possibly because in most applications the engineers don't need to worry about it (as in this case).