The LM334 is a 'programmable constant current source' (AKA constant current diode).
Looks like a transistor, costs around 70c to $1.50. Connecting a resistor between two of the legs gives you a device that lets thru a constant current (determined by the resistor) independent of the voltage (provided there is enough voltage to put the current thru the load in the first place. Kind of opposite to a zener.
When would you want this? Here's some ideas:
1. High impedance load (this is a common use for it).
2. Want to develop a known voltage across a variable resistor, but no stable power supply? Constant current solves that.
3. Maybe (havn't tried it) useful in a wah, use the variable pot resistance to control the current, which in turn drives the LEDs in a led/ldr.
4. Good for providing a constant current to your indicator led, until your battery is TOTALLY flat.

I've seen them used a couple times for cathode current programming in long tailed pair phase splitters. I also used a few of them for temperature sensing in the days before Dallas one-wire parts. RadioShack used to sell LED thermometer units that allowed you to hook up multiple remote sensors which were all built around LM334s.

This came up a few months back in a thread about tube vs. opamp sound: I have to wonder if part of what we like in the character of tube circuits is some mojo that comes from using passive resistors in all their imperfectness for current sources rather than the active sources found in opamps?

There are two styles of constant current diodes. The old one is just a pre-selected JFET with the gate shorted to the source, so what does through is Idss. It works moderately well.

The LM33x diodes are integrated circuit constant current sources. They are very close to the LM317 voltage regulator in operation. In fact, the LM317 makes a dandy constant current source that you program with one resistor also. These things are designed to put 1.25V across a resistor, and regulate current to do that. The 1.25V is a band gap reference inside the device, and the resistor determines the current because if it has 1.25V across it, the current must be fixed. They are temperature sensitive as witness their use for a temperature sensor. The LM334 may deviate a bit in particulars, but that's how it works.

Item 1 is a good use. They're a bit hissy, like all constant current devices, though.
Item 2 is the LM317 use. This is the fundamental way the LM317 operates.
Item3 is OK. There are other ways to do a variable current source, but this works.
Item 4 is good. Be aware that the CC device dissipates all the power in the circuit, so you get P = (Vsupply-Vled)*Iled in the CC device all the time. It's not a problem with 9V stuff, but at higher voltages you can exceed the 100mw of a typical TO92 package pretty easily.

There are some quite simple transistor CCSs if you want to experiment. Read up on them at the Elliot Sound Products site.

Go see Charles R. Fischer's post-humously published article at GGG: http://www.generalguitargadgets.com/index.php?option=content&task=view&id=174&Itemid=200

The LM334 figures VERY heavily in this circuit. We've ignored it for too long.

I agree these types of devices are not considered as readily as they perhaps should be, but, as RG pointed out,

> Item3 is OK. There are other ways to do a variable current source, but this works.

Normal transistors (BJTs) can be used as current sources - just look at a number of differential amplifier circuits.   In most case transistors are precise enough.

and add,

Item 5. The current is not constant with temperature, it is proportional to absolute temperature.  That's why these devices can be used as convenient temperature probes.  To make the current constant you need to modify the set-up, the app. notes show how but you can do better.   With some added circuitry, I've used these devices for temperature independent constant current sources.

There are aspects of these devices which ease design but I would not  use them for the sake of using them, especially if there is a simpler means of obtaining the same result.

Thanks for the feedback, guys! I'm not worried about the temp variation (over the range that I'm using them). I've avoided using roll- your-own transistor & fet based constant current soutrces because of component variation (for the simpler ones) and complexity (for the more complex ones). I just happened to need a very low component count solution (yeah, ordered boxes too small ) so I'm happy with my 1.5 by 2 cm.

I should have added, the + supply voltage was varying from 11 to 17 volts, which I think would be a problem for most simple constant current circuits.

http://www.diytube.com/st70/diytube_st70_manual_print.pdf
LM3xx in tube-circuit...

Puretube, when I saw you had posted I asssumed it would have been about the "tube" constant current device:
"A barretter is a bit more than a fancy resistor, its a constant current device. I believe it has an iron wire filament in a hydrogen atmosphere and it is possible for the voltage accross it to be varied quite a bit with little change in current through it. "
There would be a good physics project in saying how it works!

information lost...

National Semi used to make some "constant-current LEDs"... the name NSL32 comes to mind, but could be wrong.
These are designed to be connected directly across a power supply without needing limiting resistors. Probably supply a constant current in the range of 5 - 10 mA, might be suitable for your application(?)
Cheers, Mike