I've had some transistors of the same type with a gain of anywhere between 200 to 300 with the same IB and IC loads.

 

This circuit might be worth a try, it should be better than a resistor with a regulated 5V supply. It can probably be improved upon, but it performs OK in simple simulations.
Start with the variable resistor set at low resistance and you can monitor the current through the LED as you adjust it by measuring the voltage across the 1 ohm resistor: 1mV = 1mA
I think pretty much any NPN transistor should be OK.

 

I'll say it again--if your circuit depends on the exact forward voltage of an LED, you haven't got a good design. You can measure it for your own knowledge, and to make sure that your power supply can drive it, but you shouldn't depend on it being predictable.

I used to depend on Vf when I initially started into electronics. But then later, I learned from this forum itself a couple of years back that it should be dependent on current limiting so that Vf will follow. It was then that I learned that Led's are current sensitive devices rather than voltage! From then, I depend on current primarily, but after doing that, I DO check the voltages to make sure everything is well, else I wouldnt have found this fault. These leds were new to me and before I could even get the current to my led spec, voltage was way beyond limits. Then realized it was a regulator chip tolerance prob.!

 

This circuit might be worth a try, it should be better than a resistor with a regulated 5V supply. It can probably be improved upon, but it performs OK in simple simulations.
Start with the variable resistor set at low resistance and you can monitor the current through the LED as you adjust it by measuring the voltage across the 1 ohm resistor: 1mV = 1mA
I think pretty much any NPN transistor should be OK.

Wow, thats one interesting design I have seen without zenners!! I'll definitely try this one. Just a doubt, can it take variable/unregulated input? If so, on higher voltage inputs, will the transistor have to deal with the voltage dropped and heat up? But anyways, thanks a lot for this!

 

Wow, thats one interesting design I have seen without zenners!! I'll definitely try this one. Just a doubt, can it take variable/unregulated input? If so, on higher voltage inputs, will the transistor have to deal with the voltage dropped and heat up? But anyways, thanks a lot for this!

It's only any use with a regulated supply, if the supply was much higher than 5V then the transistor would need to be more highly rated and would waste a lot of power. With the suggested values and at 150mA with a Vf of 3.6V (worst case), the resistor will use 0.15V*0.15A=22.5mW and the transistor will use 1.25V*0.15A=188mW (plus a little for the base curent) which is within the specifications of most transistors.
It's not perfect, the current will vary slightly for different transistor gains (hence the variable resistor), and temperature change of the transistor will change the current slightly as well.