Paul__B:
Please do not advise people to use those obsolete ICs!
Any suggestion for replacement? 500 mA per channel; can be driven with 3.3V signals?
wvmarle:
Any suggestion for replacement? 500 mA per channel; can be driven with 3.3V signals?
Well, there is a CMOS substitute (pin for pin) of the ULN2803, limited to 16 V but I have mislaid the reference to it. And I had a Hard Drive crash (apparently the control board, not the disk!) a few weeks ago and lost a lot of stuff. (Yes, I know, it was getting flaky and I was too slow to copy the home directory wholesale. 
)
As I said, if you do not need PWM, the TPIC6A595 is more sensible overall. For PWM, just logic level FETs.
A single IC is more convenient than a MOSFET, two resistors and a diode for every single channel... one part vs. 32 parts.
Lots of similar darlington arrays, no similar MOSFET arrays.
Paul__B:
In the meantime however, he can use his 2N2222s, two at a time in a "not Darlington" pair configuration something like this:
(Only diagram that I can find to illustrate this configuration!) Note that not explicitly included in this diagram, you require a current limit resistor in series with the first base, 1k or so should be fine. The resistor in the collector of the first transistor (which goes to your 5 V, not 3.3) sets the base current of the second, so we are looking at 30 mA for a 300 mA final load, 180 Ohm. The load resistor illustrated will be incorporated int the LED strip.
On the 2N2222 that is actually controlling the lights.
Can you advise the voltage at the collector ?
OP said he has a 5V power supply and only a 3V3 signal voltage available.
Red led is 148.3 ohms = (5v-2.03v)/.02A so I get 2.97 volts
Blue is 100 ohms
Green is 100ohms
Second question : what is the voltage at the base of the second transistor ?
if one inverts the signal. then 5V will be on the gate of the second transistor.
(note : this layout is for example, not use, should show 5V and the resistors are not selected for this application.
Third : although we will never get a data sheet for a 'LED from WalMart' most LED's can be pulsed with higher current. Goes to POV (persistence of vision) Within the limits of the power supply and the transistor, it might be possible to get a bit more brightness from the LED's without risking over heating or damage.
Sparkfun LED data sheet shows 30mA at 10% duty cycle @ 10KHz
Paul__B:
His LEDs operate from 5 V and he is concerned about the brightness. The Darlingtons will lose about 1.5 V bringing the LED strip voltage down to 3.5. These chips are not suitable for controlling 5 V devices, and only barely suitable for 12 V devices where you can allow for the voltage loss. Please consider them simply obsolete; replacement/ repair parts only!
Could one not just use a 6.5V supply to compensate for the voltage drop through the Darlingtons?